StatPad Installation and User Guide

Skyline Technologies presents

StatPadTM

Quick and Easy Data Analysis Using Excel

0

5

10

15

2004 2006 2008 2010 2012 2014

Am

azo

n R

even

ue

($b

illi

on

s)

Time

Revenue

Trend

Forecast

Copyright 1988, 1997, 2000, 2003, 2011 by Skyline Technologies, Inc.

StatPad is a trademark of Skyline Technologies, Inc.

Excel is a registered trademark of Microsoft Corporation.

2 What is StatPad?

Table of Contents

What is StatPad? ..............................................................................................................................4

How to Install StatPad .....................................................................................................................5

How to Use StatPad .........................................................................................................................6

Overview of StatPad Features ........................................................................................................12

One-Sample Analysis .....................................................................................................................18

Summaries................................................................................................................................18

Histogram .................................................................................................................................19

Histogram (With Customized Bin Width and Landmark) .......................................................20

Box Plot ...................................................................................................................................21

Cumulative Distribution ..........................................................................................................22

Confidence Interval ..................................................................................................................23

Confidence Interval (One-Sided, 99%) ....................................................................................24

Hypothesis Test ........................................................................................................................25

Hypothesis Test (One-Sided) ...................................................................................................26

Percentile ..................................................................................................................................27

Percentile Ranking ...................................................................................................................28

Sampling ........................................................................................................................................29

Random Sample Without Replacement ...................................................................................29

Random Sample With Replacement ........................................................................................30

Uniform Distribution ...............................................................................................................31

Normal Distribution .................................................................................................................32

Binomial Distribution ..............................................................................................................33

Binomial Percentages ...............................................................................................................34

Probability Calculations .................................................................................................................35

Normal Probability (Greater Than) ..........................................................................................35

Normal Probability (Between) .................................................................................................36

Binomial Probability (Equal to) ...............................................................................................37

Binomial Probability (This or Less) .........................................................................................38

Binomial Percent (Equal to) .....................................................................................................39

Binomial Percent (Between) ....................................................................................................40

Poisson Probability (Equal to) .................................................................................................41

Poisson Probability (This or Less) ...........................................................................................42

Exponential Probability (This or More) ...................................................................................43

Exponential Probability (Between) ..........................................................................................44

Discrete Probability ..................................................................................................................45

Two-Sample Analysis ....................................................................................................................46

Summaries................................................................................................................................46

Histograms ...............................................................................................................................47

Box Plots ..................................................................................................................................48

Confidence Interval ..................................................................................................................49

Hypothesis Test ........................................................................................................................50

Many-Sample Analysis ..................................................................................................................51

Summaries................................................................................................................................51

Histograms ...............................................................................................................................52

Box Plots ..................................................................................................................................53

F Test for One-Way ANOVA ..................................................................................................54

Mean Differences .....................................................................................................................55

Bivariate Analysis ..........................................................................................................................56

Scatterplot ................................................................................................................................56

Scatterplot with Least-Squares Line ........................................................................................57

Correlation ...............................................................................................................................58

Correlation with Test ...............................................................................................................59

Regression ................................................................................................................................60

Predicted and Residuals ...........................................................................................................61

Univariate Summaries ..............................................................................................................62

Histograms ...............................................................................................................................63

Box Plots ..................................................................................................................................64

Multivariate Analysis and Multiple Regression ............................................................................65

Scatterplots ...............................................................................................................................65

Correlations ..............................................................................................................................66

Multiple Regression .................................................................................................................67

Predicted and Residuals ...........................................................................................................68

Diagnostic Plot .........................................................................................................................69

Univariate Summaries ..............................................................................................................70

Histograms ...............................................................................................................................71

Box Plots ..................................................................................................................................72

Time-Series Analysis .....................................................................................................................73

Trend-Seasonal ........................................................................................................................73

Forecast with Series .................................................................................................................74

Moving Average (Smooth) ......................................................................................................75

Seasonal Index .........................................................................................................................76

Seasonally Adjusted Series ......................................................................................................77

Long-Term Trend .....................................................................................................................78

Seasonalized Trend ..................................................................................................................79

A Combination: Data Series With Long-Term Trend and Forecast ........................................80

Numeric Output .......................................................................................................................81

Quality Control ..............................................................................................................................82

X-Bar, R Charts (No Standard Given) ......................................................................................82

X-Bar, R Charts (Standard Given) ............................................................................................83

Percentage or Count Chart (No Standard Given) .....................................................................84

Percentage or Count Chart (Standard Given) ..........................................................................85

4 What is StatPad?

What is StatPad? Welcome to StatPad1, a software system designed for people who wish to perform statistical

analysis within their Microsoft Excel2 computer spreadsheets. StatPad was designed to make

statistical analysis as accessible, painless, and easy to understand as possible by bringing basic

statistical analysis and its interpretation into the environment where business and other data are

often found: namely within an Excel spreadsheet. Whenever possible, the analysis is guided by

choices from a dialog box that adapts itself automatically to your situation. The results,

consisting of charts, explanatory text, and computations, then become part of your worksheet.

StatPad will perform all aspects of basic statistics: design using a random sample, exploration

through graphic representations of data, estimation with summaries and confidence intervals

(both one-and two-sided at various confidence levels), hypothesis testing, normal and binomial

probability calculations, multiple regression analysis, trend-seasonal time series analysis, and

statistical quality control charts.

Heres how to get started if you are in a hurry: after you open the file STATPAD.XLA, you will

find StatPad listed under the Excels Add-Ins Ribbon (or Tools menu for older versions of Excel)

ready for you to select. When selected, StatPad greets you with its main dialog box, ready for

analysis.

1StatPad is a trademark of Skyline Technologies, Inc.

2Excel is a registered trademark of Microsoft Corporation.

How to Install StatPad 5

How to Install StatPad All you need in order to run StatPad is a computer running Microsoft Excel for Windows. There

are two ways to install StatPad, depending upon whether or not you want StatPad to be there

automatically whenever you work in Excel. Please begin by copying the file STATPAD.XLA to a

folder on your computer.

If you wish StatPad to be available automatically when you run Excel:

1. In Excel, choose File/Options, select Add-Ins at the left, wait a moment, then choose

"Go" near the bottom to manage Excel Add-Ins (Excel 2007 users will start by clicking

on the OfficeButton at the top left, choose ExcelOptions at the bottom before continuing

by selecting Add-Ins at the left and choosing "Go").

2. Browse to the folder where you put the file STATPAD.XLA, select the file, and click OK.

3. Be sure the StatPad entry is checked in the list of add-ins, then choose OK.

4. StatPad will be available in the Add-Ins Ribbon near the top (or Tools menu for older

versions of Excel).

If you wish to load StatPad manually each time you open Excel:

Either double-click the file STATPAD.XLA or use Excels File Open menu commands to

open this file from its folder on your computer. Choose Enable Macros if necessary.

The choice StatPad will then be available under Excels Add-Ins Ribbon (or Tools menu

for older versions of Excel). StatPad will remain available until you close Excel.

If you need to change Excel's macro security level, you will find this at File / Options /

TrustCenter / TrustCenterSettings / Add-Ins.

6 How to Use StatPad

How to Use StatPad Heres how to use StatPad:

1. Get into Excel and bring your data (if any) into the worksheet.

2. If StatPad has already been installed, simply select StatPad from Excels Add-Ins Ribbon

near the top of the screen to begin statistical analysis.

If StatPad has not yet been installed, either open the file STATPAD.XLA using Excels File

Open menu command near the top of the screen or read the previous section How to

Install StatPad to see how to make StatPad available whenever you are in Excel.

3. You will see StatPads main dialog box, ready to guide you through the analysis:

4. Select a situation from the list near the top left (One Sample, Sampling, Probability, Two

Sample, Many Sample, Bivariate, Multivariate, Time Series, or Quality Control).

5. Select the analysis you want from the list near the top right. Note that this analysis list

changes automatically for you, depending on the situation you choose. For a One Sample

situation, the analysis choices are Summaries, Histogram, etc. But if you select

Probability instead, the analysis choices instantly change to Normal Probability, Binomial

Probability, and Binomial Percent.

6. Give StatPad the additional information it needs. StatPad will automatically change to

show you what is needed, so you may fill in the blanks as they appear. For One Sample,

Summaries, you need to give StatPad a data set name and an output range. For One

Sample, Confidence Interval, so that you can tell StatPad which confidence level you

How to Use StatPad 7

wish, an edit box will appear automatically for this purpose (you may also decide to

choose a one-sided interval). Heres how the main dialog box changes:

For a multiple regression analysis, StatPads main dialog changes again (automatically!)

allowing you to select the X variables (for example, income, percent male, and

readership) to use to explain the Y variable (for example, the cost of a full-page color

magazine ad).


7. Heres how to select your data set(s) from the list(s). StatPad puts into its lists each Excel

range name that identifies a single column of numbers.3 When you name your data with

StatPad, the name also becomes an Excel range name.

a. If just one data set is needed (e.g., for one-sample analysis), you may choose one of

the following:

i. Click on its name, in the list.

or

ii. Type its name into the edit-box, just above the list.

or

iii. Click on the edit-box, just above the list, and then drag in the worksheet with the

mouse to identify your column of numbers. This is useful for a quick analysis

when you do not care to use a name to identify the data.

b. If more than one data set can be specified (e.g., many-sample analysis, or the X

variables for a multiple regression), you may choose one of the following:

i. Click on each name that you wish to select, scrolling up and down as needed. If

you click again on a selected name, it is unselected (be careful not to click quickly

twice on the same name; Excel will interpret this as a double-click and StatPad

will immediately begin the analysis).

or

ii. Move through the list using the cursor (arrow) keys, selecting and unselecting by

hitting the spacebar.

8. If your data are in the worksheet, but are not offered to you as a choice4 in StatPads lists,

heres how to proceed:

a. Click on StatPads Add Data button (at the right, just above the middle of StatPads

main dialog box) to put a data set name into the list. You then see the following

dialog box, and you may drag with the mouse to select the data (one column of

numbers) and specify the name you want. This name will then appear in StatPads

lists along with the other data sets.

3Heres a quick way to find out the name (if any) associated with a list of numbers. Highlight the list (drag with the

mouse), then look for the name in Excels Name Box near the top left corner of the worksheet. StatPad limits the size

of a each list to a maximum of 65,000 numbers.

4If you have used Excel to name a column of numbers (e.g., with Excels Insert Name Define menu items), this name

will appear automatically in StatPads list. When you name a column of numbers within StatPad, this name also

becomes an Excel range name for your data. Names can be deleted using Excels Insert Name Define Delete menu

items.


Heres how the screen might look after you (1) click in the Range box of the above

dialog box, (2) highlight your data in the worksheet, (3) click in the Name box of the

dialog box, and (4) type in the name (Prices for this example, but please dont use

spaces or special characters):

b. Alternatively, you may feel free to type a name for the data set into the edit-box in

StatPads main dialog box, even if that name is not proposed for you. This can be

done whenever only one data set can be used for the chosen situation (but please dont

use spaces or special characters in the name). Once you hit Enter, click on Do It, or

double click, to begin the analysis, StatPad will ask you to select the column of

numbers you want, using the following dialog box. After this, the name will

automatically show up in StatPads data set lists.


9. Use the Output Range box at the lower right of the main dialog box to tell StatPad where

to put the results.

a. If youve asked for a chart:

i. If you provide a single cell as the Output Range, then StatPad will place a chart of

the default size with upper-left corner at this cell.

ii. If you provide a rectangular range of cells as the Output Range, then StatPad will

make the chart the same size as your range.

b. If youve asked for numbers and text:

i. If there is enough room without erasing any of your data, StatPad will place the

upper-left cell of the output at the Output Range you specified.

ii. If your results would overwrite any of your data, StatPad will give you the option

of either specifying a different Output Range, or (use caution!) going ahead and

erasing some of your data to make room for the results if you wish.

10. After StatPad performs the analysis you requested (or asks for clarification, if needed),

you will again find the StatPad main dialog box on your screen, ready for further analysis.

You may either continue your analysis with StatPad, or leave StatPad (select Cancel or

hit the Esc key) to return control to Excel and your worksheet.

11. You can format StatPads results because they are part of your Excel spreadsheet, after

leaving the StatPad dialog box by hitting the Esc key or selecting Cancel.

a. You can select and format numbers in individual cells as you ordinarily would in

Excel (for example, using the Number Group of the Home Ribbon). For example, you

can format with dollar signs, set the number of decimal places, format as percentages,

etc.

b. You can customize StatPads charts as you would for any Excel chart. For example,

you might select the chart and then use the Chart Tools Ribbons (Design, Layout, and

Format) at the top of the Excel window. Another method would be to double-click the

part of the chart you wish to change, for example the x axis, to bring up the relevant

formatting options. You might then choose set the scale under Axis Options (e.g., to

change the minimum and/or maximum) or select Number (e.g., to change the number

formatting).


12. You can copy StatPads results to your word processor, after leaving the StatPad dialog

box by hitting the Esc key or selecting Cancel.

a. To copy text and numbers to your word processor, proceed as follows:

i. Highlight your cell(s) and choose Copy from the Clipboard Group of the Home

Ribbon.

ii. Activate your word processor and move the cursor to where you want the results

to go.

iii. Depending upon your word processor, you may wish to paste as unformatted text.

The text then becomes part of the text document and you may format it as you

like. For example, with Microsoft Word 2010, you might click on the word

"Paste" in the Clipboard Group of the Home Ribbon, then choose Paste Special

from the Paste Options, to obtain the Unformatted Text choice.

b. To copy charts to your word processor, proceed as follows:

i. Click on the edge of a chart (just one at a time) to select it, then choose Copy from

the Clipboard Group of Excel's Home Ribbon.

ii. Activate your word processor and move the cursor to where you want the chart to

go.

iii. Depending upon your word processor, you may wish to paste as a Picture

(instead of as an Excel object). The chart then becomes part of the text document

and you would be able to place and size it using your word processors

commands. For example, with Microsoft Word 2010, you might click on the

word "Paste" in the Clipboard Group of the Home Ribbon, then choose Paste

Special from the Paste Options, to obtain the Picture (Enhanced Metafile)

choice.

13. For more information about statistical analysis, its applications and interpretation, please

consult a book such as Practical Business Statistics by Andrew F. Siegel (Elsevier /

Academic Press, sixth edition, 2012).

12 Overview of StatPad Features

Overview of StatPad Features StatPads statistical analyses are grouped into the following situations:

One Sample

Sampling

Probability

Two Sample

Many Sample

Bivariate

Multivariate

Time Series

Quality Control

These situations are presented in a list at the left in StatPads main dialog box. When you select a

situation, the appropriate analyses are available in a list to the right in this dialog box. When you

select a situation and analysis, an explanation also appears in the dialog box and the dialog box

changes to allow you to specify what is needed for the analysis (e.g., a confidence level). Here is

a list of the situations, analyses, and explanations available within StatPad. More details about

each one, with an example, are given on the pages that follow.

One Sample

Summaries Compute statistical summaries for the data: count, average or mean, median,

smallest, largest, quartiles, standard deviation, and standard error.

Histogram Draw a histogram to explore the data, showing the shape of the distribution,

typical values, variability, and outliers. Data are concentrated where the

histogram bars are high. Check 'Customize' to specify optional bin width and

landmark point.

Box Plot Draw a box plot to explore the data, showing the 5-number summary (smallest,

lower quartile, median, upper quartile, and largest). In the ordinary box plot, a

line extends from the box on each side to the most extreme value. Check

Detailed box plot to indicate outliers separately and have the lines extend from

the box on each side to the most extreme value (adjacent value) that is not an

outlier.

Cumulative

Distribution

Draw a cumulative distribution function for the data, showing the percentage of

data values less than each given number. This shows you the percentiles.

Overview of StatPad Features 13

Confidence

Interval

Compute a confidence interval for the population mean. This is statistical

inference about the population, based on random sampling. Two-sided or one-

sided interval, with your chosen confidence level.

Hypothesis

Test

Test the null hypothesis that the population mean is equal to a given reference

value. This is statistical inference about the population, based on random

sampling. Two-sided or one-sided testing (Student's t test) is used.

Percentile Given a percentage, find the percentile value. This data value has approximately

this percentage of the data values smaller than it.

Percentile

Ranking

Find the percentage ranking for a given value. This is the approximate

percentage of data values that are less than the given value.

Sampling

Sample

Without

Replacement

Select a random sample from a larger population, without replacement so that

no item can be selected more than once. All population items are equally likely

to appear in the sample, and they are chosen independently of one another.

Sample With

Replacement

Select a random sample from a larger population, with replacement so that an

item may be selected more than once. All population items are equally likely to

appear in the sample, and they are chosen independently of one another.

Uniform

Distribution

Select a random sample from a uniform distribution, where all values are

equally likely between the smallest and largest possible value. By specifying a

name, you will be able to easily use the result later.

Normal

Distribution

Select a random sample from a normal distribution, given the mean and

standard deviation. By specifying a name, you will be able to easily use the

result later.

Binomial

Distribution

Select a random sample from a binomial distribution (the number of

occurrences) given the number of trials and the probability of occurrence. By

specifying a name, you will be able to easily use the result later.

Binomial

Percentages

Select a random sample of binomial percentages, given the number of trials and

the probability of occurrence. By specifying a name, you will be able to easily

use the result later.


Probability

Normal

Probability

Probabilities for a normal distribution: the symmetric bell-shaped curve, given a

mean and a positive standard deviation.

Binomial

Probability

Probabilities for a binomial distribution: the number of occurrences out of a

given number of independent trials with a given probability.

Binomial

Percent

Probabilities for a binomial percentage, given the number of independent trials

and the probability for each trial.

Poisson

Probability

Probabilities for a Poisson distribution: the number of random occurrences

where the rate is fixed, given the mean number. For example, the number of

orders you will receive next week, if orders occur at a constant rate with an

average of 5 per week.

Exponential

Probability

Probabilities for an exponential distribution: a highly skewed distribution with

no memory, given the mean. For example, the length of a telephone call or the

time until the next customer arrives where the mean is 9 minutes.

Discrete

Probability

Mean (expected value) and standard deviation for a discrete random variable,

given a set of values and their associated probabilities.

Two Samples

Summaries Compute univariate summaries for each data set. Also find the average

difference and its standard error. If sample sizes are identical, you may indicate

that a pair of measurements was made on each item.

Histograms Draw a histogram for each data set, for data exploration.

Box Plots Draw a box plot for each data set, for data exploration, using the same scale for

comparison. In the ordinary box plot, a line extends from the box on each side

to the most extreme value. Check Detailed box plot to indicate outliers

separately and have the lines extend from the box on each side to the most

extreme value (adjacent value) that is not an outlier.

Confidence

Interval

Compute a confidence interval for the population mean difference. This is

statistical inference. Two-sided interval, with chosen confidence level. If

sample sizes are identical, you may indicate that a pair of measurements was

made on each item.

Hypothesis

Test

Test the null hypothesis that the population mean difference is zero. This is

statistical inference. Two-sided testing using Student's t test. If sample sizes are

identical, you may indicate that a pair of measurements was made on each item.


Many Samples

Summaries Select as many data sets as you wish. Compute univariate summaries for each.

Histograms Draw a histogram for each sample, for data exploration.

Box Plots Draw a box plot for each sample, for data exploration, using the same scale for

comparison. In the ordinary box plot, a line extends from the box on each side

to the most extreme value. Check Detailed box plot to indicate outliers

separately and have the lines extend from the box on each side to the most

extreme value (adjacent value) that is not an outlier.

F Test One-way analysis of variance (ANOVA). Test the null hypothesis that the

population means are all identical. This is statistical inference.

Mean

Differences

Confidence intervals and hypothesis tests for the difference of each pair of

population means (least-significant-difference test). This is statistical inference.

Bivariate

Scatterplot Draw a scatterplot to explore the relationship between two variables.

Scatterplot

with Line

Draw a scatterplot with least-squares line to explore the relationship between

two variables.

Correlation Find the strength of the relationship between two variables as a pure number

where 1 indicates a perfect increasing relationship, -1 a perfect decreasing

relationship, and 0 suggesting no relationship.

Correlation

with Test

Find and test the strength of the relationship between two variables. This is

statistical inference.

Regression Predict the dependent Y variable from the independent X variable using a

straight-line relationship.

Predicted and

Residuals Predicted values of Y based on X, the residual difference: Actual Y Predicted

Y, and the standardized residuals.

Univariate

Summaries

Compute univariate summaries for each variable.

Histograms Draw a histogram for each variable, for data exploration.


Box Plots Draw a box plot for each variable, for data exploration. In the ordinary box plot,

a line extends from the box on each side to the most extreme value. Check



outlier.

Multivariate

Scatterplots Select as many X variables as you wish, but just one Y variable. Draw

scatterplots for all pairs of variables to explore their relationships.

Correlations Find the strength of the relationship between pairs of variables as a matrix of

correlation coefficients (1 is perfect positive correlation, 1 is perfect negative

correlation, and 0 suggests no relationship).

Regression Prediction of the dependent Y variable from the independent X variables using a

linear relationship.

Predicted and

Residuals

Predicted values of Y based on the X variables, the residual differences (Actual

Y Predicted Y) and the standardized residuals.

Diagnostic

Plot

Look for problems in the regression linear model, such as unequal variability or

nonlinearity.

Univariate

Summaries

Compute univariate summaries for each variable.

Histograms Draw a histogram of each variable, for data exploration.

Box Plots Draw a box plot of each variable, for data exploration. In the ordinary box plot,

a line extends from the box on each side to the most extreme value. Check



outlier.

Time Series

Trend-

Seasonal

A decomposition into (1) long-term trend (linear or exponential), (2) repeating

seasonal component (monthly or quarterly), (3) wandering cyclic component,

and (4) irregular component. Seasonal adjustment & forecasting. Time must

increase down data column.


Quality Control

X-Bar, R

Charts

Chart the averages and the ranges of your data to see if this process is in or out

of control. Choose a subgroup size from 2 to 25. You may specify a standard if

one is available.

Pct, Count

Chart

Chart the percents or counts to see if this process is in or out of control. Your

data may be either counts or percentages (counts divided by the sample size).

You may specify a standard if one is available.


One-Sample Analysis

Summaries

Summaries are used to give you selected

numbers that represent and describe your

data set.

StatPads summaries (below) for Quality

scores show how many data values there are

(n = 50), typically how high the scores are

( 1 /n

iiX X n

=90.78), and about how

far individual scores are

( S X X niin

( ) / ( )21

1 = 7.56) from

the mean. The quartiles are about 1/4 of the

way in from each end (highest and lowest)

while the median is 1/2 way in. The standard

error of the average is S S nX / .

To compute the summaries using StatPads main dialog box, select One Sample as the

situation and Summaries as the analysis. Select your data from the list (or use Add Data if your

column of numbers is in the worksheet but is not in the list), check the Output Range to be sure

that is where you want the results to appear, and then select Do It (or hit the Enter key).

Quality Summaries

50 Count n

90.78 Mean or average

7.56 Standard deviation (variability of individuals)

72 Smallest

86 Lower quartile

93 Median

97 Upper quartile

99 Largest

1.069 Standard error (variability of sample average, if random sample)


Histogram

The histogram is used to visually explore

a data set. The data axis is horizontal, and

the bars show how many data values are

within each interval. Data are concentrated

where bars are tall. You can see typical

value, variability, and distribution shape.

StatPads histogram (below) shows that

the Quality scores fall within the interval

from about 70 to 100. They are skewed with a

long tail towards lower values, being more

concentrated in the higher end of the range.

To create a histogram using StatPads

main dialog box, select One Sample as the

situation and Histogram as the analysis. Select your data from the list (or use Add Data if your

column of numbers is in the worksheet but is not in the list), check the Output Range, and then

select Do It.

StatPad chooses a default bin width and landmark (which could be a left or right endpoint

of the histogram, or any bin boundary) for the histogram bars. These can be changed using the

Customize check-box (see next item). Note that Excel (not StatPad) chooses the minimum and

maximum horizontal scale. These may be changed (as was done for the chart below) by leaving

StatPad by hitting the Esc key or selecting Cancel, then double-clicking on the axis to find

Minimum and Maximum as Axis Options.

0

10

20

60 70 80 90 100

Fre

qu

ency

Quality


Histogram (With Customized Bin Width and Landmark)

There are often several reasonable

choices for how wide to make the histogram

bars and where to place them left-to-right.

StatPad can choose a default bin width and

landmark for the histogram bars, or you can

specify customized values.

In the customized histogram below, the

bin width has been decreased to 1 to show

more detail (StatPads default bin width for

this data set was 5).

To create a customized histogram using

StatPads main dialog box, select One

Sample as the situation and Histogram as the

analysis. Select your data from the list (or use Add Data if your column of numbers is in the

worksheet but is not in the list). When you click on Customize, two edit-boxes appear: for Bin

Width and for the optional Landmark. You may then click on each and type the value you wish.

The Landmark setting would shift the bars left or right to align on the specified value. Then

check the Output Range, and then select Do It.

0

5

10

60 70 80 90 100

Fre

quen

cy

Quality


Box Plot

The box plot is used to quickly and

visually explore a data set; it shows you a

central box defined by the quartiles, with the

median indicated within the box. In the

ordinary box plot, a line extends from the box

on each side to the most extreme value. In the

detailed box plot, outliers are indicated

separately and these lines extend from the

box on each side to the most extreme value

(adjacent value) that is not an outlier.

In StatPads box plot for Sensitivity

(below left) you see that the middle half of the

data extends from about 60 to 100, with the

median at about 80. The line at the right

extends to the largest at about 180.

StatPads detailed box plot (below right) shows outliers separately, revealing that the

largest value, at about 180, is an outlier.

To display a box plot using StatPads main dialog box, select One Sample as the situation

and Box Plot as the analysis. Select your data from the list (or use Add Data if your column of

numbers is in the worksheet but is not in the list). Click on Detailed box plot if you wish outliers

to be displayed separately. Then check the Output Range, and then select Do It.

Outliers are defined as data values more than 1.5 times the interquartile range away from

either quartile.

0 50 100 150 200

Sensitivity

0 50 100 150 200

Sensitivity


Cumulative Distribution

The cumulative distribution function is

used to show you the percentiles of the data.

Percentages are shown vertically (from 0 to

100%) and data values are horizontal. The

chart shows the percentage of the data values

(vertical scale) that are equal or less to the

given value (horizontal scale).

In StatPads cumulative distribution

function for Quality (below) you can see that

about 10% of the Quality scores are less than

or equal to 80, about 25% of the Quality

scores are less than or equal to 85, and that

about a third are scores of 90 or less.

To compute a cumulative distribution function using StatPads main dialog box, select One

Sample as the situation and Cumulative Distribution as the analysis. Select your data from the

list (or use Add Data if your column of numbers is in the worksheet but is not in the list), check

the Output Range, and then select Do It.

0%

20%

40%

60%

80%

100%

60 70 80 90 100

Cu

mu

lati

ve

Per

cen

t

Quality


Confidence Interval

A confidence interval for the mean

includes the unknown population mean with

known confidence, e.g., 95%. Random

sampling from a normal population is

assumed.

StatPads two-sided 95% confidence

interval results for Quality (below) tell you

that the bounds of the interval are 88.63 and

92.93.

To compute a confidence interval using


Sample as the situation and Confidence

Interval as the analysis. Select your data

from the list (or use Add Data if your column of numbers is in the worksheet but is not in the

list), check the Output Range, and then select Do It. You may also change the Confidence level

(from the default 95%) or select a one-sided interval instead of a two-sided interval (see next

item).

Confidence interval for Quality:

We are 95% sure that the

population mean for Quality

is somewhere between

88.63 and 92.93

(assuming a random sample from a normal population).


Confidence Interval (One-Sided, 99%)

The one-sided interval says, with

specified confidence, that the unknown

population mean is either at least ... (for

an upper confidence interval) or no more

than ... (for a lower confidence interval).

You should decide whether to use a one-sided

or two-sided confidence interval before you

look at the data. You should not use both

upper and lower one-sided confidence

intervals on the same data set; either use a

two-sided interval, or choose just one side for

a one-sided confidence interval. If in doubt,

use a two-sided confidence interval.

StatPads one-sided upper 99%

confidence interval for Quality (below) shows you that the bound is 88.21.

To compute a one-sided 99% confidence interval using StatPads main dialog box, select

One Sample as the situation and Confidence Interval as the analysis. Select your data from the

list (or use Add Data if your column of numbers is in the worksheet but is not in the list), click on

the 1-sided box of your choice, set the Confidence Level to 99%, check the Output Range, and

then select Do It.

One-sided upper confidence interval for Quality:

We are 99% sure that the

population mean for Quality

is at least

88.21

(assuming a random sample from a normal population).


Hypothesis Test

A hypothesis test is used to decide, based

on data, whether or not the unobservable

population mean could reasonably be equal

to a given reference value. Because the

sample average represents (with statistical

error) the unknown population mean, the

result is often stated in terms of a significant

(or nonsignificant) difference between the

sample average and the reference value, both

of which are known. Random sampling from

a normal population is assumed.

StatPads hypothesis test results for

Quality (below) show a very highly

significant difference between the reference

value (given here as 87.5) and the observed average Quality score of 90.78. Results include the t

value, the p value, the practical interpretation of the results, and a formal statement of the null

hypothesis being tested.

To perform a hypothesis test using StatPads main dialog box, select One Sample as the

situation and Hypothesis Test as the analysis. Select your data from the list (or use Add Data if

your column of numbers is in the worksheet but is not in the list), specify the Reference Value,

check the Output Range, and then select Do It. Optionally, you may specify a one-sided test

(upper or lower); see next item.

The p value says that, if the population mean had been equal to the reference value, then p is

the probability of observing such a large (or larger) difference between the sample average and

the reference value. Smaller p values indicate significance because rare events are unlikely.

.

Hypothesis test for Quality:

t = 3.07

p = 0.00350

The sample average

90.78

is highly significantly different (p


Hypothesis Test (One-Sided)

A one-sided upper hypothesis test can

decide only whether the sample average is

significantly larger than the reference value.

A one-sided lower hypothesis test can decide

only whether the sample average is

significantly less than the reference value.

You should decide whether to use a one-sided

or two-sided test before you look at the data.

You should not use both upper and lower

one-sided hypothesis tests on the same data

set; either use a two-sided interval, or choose

just one side for a one-sided hypothesis test.

If in doubt, use a two-sided test.

StatPads one-sided upper hypothesis

test results for Quality (below) show that the scores are significantly larger, on average, than the

reference value (given here as 87.5). Results include the t value, the p value, the practical

interpretation of the results, and a formal statement of the null hypothesis being tested.

To perform a one-sided hypothesis test using StatPads main dialog box, select One Sample

as the situation and Hypothesis Test as the analysis. Select your data from the list (or use Add

Data if your column of numbers is in the worksheet but is not in the list), click on the 1-sided box

of your choice, specify the Reference Value, check the Output Range, and then select Do It.

One-sided hypothesis test for Quality:

t = 3.07

p = 0.00175

The sample average

90.78

is highly significantly larger (p


Percentile

Percentiles are landmarks in the data

that are a known percentage (of the data

values) from smallest to largest. The smallest

data value is the 0th

percentile, the largest is

the 100th

percentile, the median is the 50th

percentile, and so forth.

In StatPads percentile calculation

(below) the 85th percentile for the Quality

scores is found to be a score of 98. That is,

the score 98 is about 85% of the way (in the

ordered list of scores) from the smallest to the

largest score.

To find a percentile using StatPads main

dialog box, select One Sample as the situation and Percentile as the analysis. Select your data

from the list (or use Add Data if your column of numbers is in the worksheet but is not in the

list), provide the Percentage for which you would like the percentile, check the Output Range,

and then select Do It.

For Quality:

85 th percentile

is 98


Percentile Ranking

The percentile ranking of a given data

value gives you the percentage of the way

along in the list of data values (from smallest

to largest) that this given data value is.

In StatPads percentile calculation

(below) the Quality score 87.5 is found to be

30% of the way from smallest to largest.

To find a percentile ranking using


Sample as the situation and Percentile

Ranking as the analysis. Select your data

from the list (or use Add Data if your column

of numbers is in the worksheet but is not in

the list), provide the data Value for which you would like the percentile ranking, check the

Output Range, and then select Do It.

For Quality:

87.5 is the

30 th percentile


Sampling

Random Sample Without Replacement

A random sample without replacement

is chosen from a population so that (1) all

population units are equally likely to be

chosen, (2) units are selected independently

of one another, and (3) once a unit is chosen,

it cannot be chosen again. All sampled units

are different when sampling without

replacement.

StatPads results (below) show a sample

of 5 selected at random (without replacement)

from a population of size 100. The selected

items (in order) are 19, 25, 59, 67, and 89.

This list of five numbers has also been given a

name (firstSample was chosen here) which

will appear in StatPads lists of data sets.

To select a random sample without replacement using StatPads main dialog box, select

Sampling as the situation and Sample Without Replacement as the analysis. Specify a

Population Size and a Sample Size. Provide an optional name for the resulting data in case you

plan to refer to it later, check the Output Range, and then select Do It.

Random sample of size 5

from population numbered from 1 to 100

chosen without replacement:

firstSample

19

25

59

67

89


Random Sample With Replacement

A random sample with replacement is

chosen from a population so that (1) all

population units are equally likely to be

chosen, (2) units are selected independently

of one another, and (3) once a unit is chosen,

it is replaced so that it may be chosen again.

The sampled units may or may not all be

different when sampling with replacement.

The StatPad results below show a sample

of 5 selected at random (with replacement)

from a population of size 100. The selected

items (in order) are 43, 51, 55, 55, and 82. Note that an item (55) was chosen twice. This can

happen when sampling with replacement. This

list of five numbers has also been given a name (secondSample was chosen here) which will

appear in StatPads lists of data sets.

To select a random sample with replacement using StatPads main dialog box, select

Sampling as the situation and Sample With Replacement as the analysis. Specify a Population

Size and a Sample Size. Provide an optional name for the resulting data in case you plan to

refer to it later, check the Output Range, and then select Do It.


from population numbered from 1 to 100

chosen with replacement:

secondSample

43

51

55

55

82


Uniform Distribution

A uniform distribution generates

numbers, chosen independently of one

another, that are equally likely to fall

anywhere within a specified interval.

In StatPads results (below) five numbers

were selected uniformly from 35 to 45. This

list of five numbers has also been given a

name (uniformSample was chosen here)

which will appear in StatPads lists of data

sets.

To select a uniform sample using

StatPads main dialog box, select Sampling

as the situation and Uniform Distribution as

the analysis. Specify the Smallest and Largest values of the distribution. Specify the Sample

Size. Provide an optional name for the resulting data in case you plan to refer to it later, check

the Output Range, and then select Do It.


selected from a uniform distribution from 35 to 45:

uniformSample

37.28

41.19

39.90

41.81

43.87


Normal Distribution

A normal distribution generates

numbers, chosen independently of one

another, that follow a bell-shaped

distribution, with values most likely to fall

near the mean and the width of the bell

defined by the standard deviation (Std dev).

Observations fall within one standard

deviation of the mean about 68% of the time.


were selected from a normal distribution with

mean 65 and standard deviation 20. This list

of five numbers has also been given a name

(simulatedScores was chosen here) which

will appear in StatPads lists of data sets.

To select a normal sample using StatPads main dialog box, select Sampling as the

situation and Normal Distribution as the analysis. Specify the Mean and Standard Deviation

(Std dev) values of the distribution. Specify the Sample Size. Provide an optional name for the

resulting data in case you plan to refer to it later, check the Output Range, and then select Do It.


selected from a normal distribution with mean 65 and standard deviation 20:

simulatedScores

49.78

69.27

58.02

88.10

63.90


Binomial Distribution

A binomial distribution is used to

describe the number of times an event

happens out of n trials, where each trial was

performed independently with a fixed

probability.


are selected from a binomial distribution with

10 trials each having probability 0.5 of

success. In the first of the five samples, there

were 4 out of 10 successes. In the second

sample, 6 of 10 were successful.

To select a binomial sample using

StatPads main dialog box, select Sampling

as the situation and Binomial Distribution as the analysis. Specify the Number n of trials and

the Probability of each trial. Specify the Sample Size. Provide an optional name for the resulting

data in case you plan to refer to it later, check the Output Range, and then select Do It.

Random sample of size 5 selected from a binomial distribution

representing the number of successes in 10 trials, each with probability 0.5:

4

6

6

5

6


Binomial Percentages

Binomial percentages describe the

percent or proportion of the time an event



probability.

In StatPads results (below) five binomial

percents were selected from a distribution

with 10 trials each having probability 0.5 of

success. In the first of the five samples, 0.3 or

30% of the 10 trials were successful. In the

second sample, 60% of the 10 were

successful.

To select a sample of binomial

percentages using StatPads main dialog box, select Sampling as the situation and Binomial

Percentages as the analysis. Specify the Number n of trials and the Probability of each trial.

Specify the Sample Size. Provide an optional name for the resulting data in case you plan to

refer to it later, check the Output Range, and then select Do It.

Random sample of size 5 selected from a binomial distribution

representing the percentage of successes in 10 trials, each with probability 0.5:

0.3

0.6

0.4

0.8

0.3


Probability Calculations

Normal Probability (Greater Than)

A normal distribution generates numbers

according to a bell-shaped distribution, with

values most likely to fall near the mean and

the width of the bell defined by the standard

deviation. Observations fall within one

standard deviation of the mean about 68% of

the time. Probabilities for a normal

distribution are given by the area under the

bell-shaped curve.

StatPads result (below) shows the

probability (0.401) that the specified normal

distribution (with mean 75 and standard

deviation 20) is greater than the given value

(80).

To find a normal probability using StatPads main dialog box, select Probability as the

situation and Normal Probability as the analysis. Choose the type of probability you want

(Greater than, Less than, Between, or Not between), then give the Value(s) requested. Specify the

Mean and Standard Deviation of the normal distribution. Check the Output Range, and then

select Do It.

The probability that a normal random variable

with mean 75 and standard deviation 20

is greater than 80 is:

0.401


Normal Probability (Between)

When you ask StatPad to find the

probability of being between (or not

between), the dialog box changes to allow

you to specify the two values, lower and

upper.


probability (0.175) that the specified normal

distribution (with mean 75 and standard

deviation 20) is between the two given values

(80 and 90).

To find a normal probability using

StatPads main dialog box, select Probability

as the situation and Normal Probability as

the analysis. Choose the type of probability you want (Greater than, Less than, Between, or Not

between), then give the Value(s) requested. Specify the Mean and Standard Deviation of the

normal distribution. Check the Output Range, and then select Do It.

The probability that a normal random variable

with mean 75 and standard deviation 20

is between 80 and 90 is:

0.175


Binomial Probability (Equal to)

A binomial distribution describes the

number of times an event happens out of n

trials, where each trial was performed

independently with a fixed probability.


probability (0.205) that a specified binomial

distribution is exactly equal to 4. That is, the

probability is 0.205 of observing exactly 4

successes out of 10 independent trials with

probability 0.5 for each trial.

To find a binomial probability using


as the situation and Binomial Probability as

the analysis. Choose the type of probability you want (Equal to, This or more, This or less, or

Between), then give the Value(s) requested. Specify the Number n of trials and the Probability

for each trial of the binomial distribution. Check the Output Range, and then select Do It.

If you specify an Equal to value that is not a whole number, StatPad correctly reports the

resulting probability as zero because a binomial random variable gives the number of successes

(which must be a whole number).

The probability that a binomial random variable

with 10 repeated trials, each with probability 0.5

is equal to 4 is:

0.205


Binomial Probability (This or Less)

You can also ask StatPad to find the

probability that a binomial random variable

is This value or more, This value or

less, or Between two values.



distribution is 4 or less. That is, the

probability is 0.377 of observing exactly 0, 1,

2, 3, or 4 successes out of 10 independent

trials with probability 0.5 for each trial.

To find a binomial probability using


as the situation and Binomial Probability as


Between), then give the Value(s) requested. Specify the Number n of trials and the Probability

for each trial of the binomial distribution. Check the Output Range, and then select Do It.

The probability that a binomial random variable


is 4 or less is:

0.377


Binomial Percent (Equal to)

A binomial percentage describes the

percent or proportion of the time an event



probability.



percentage distribution is exactly equal to

70%. That is, the probability is 0.117 of

observing exactly 70% successes out of 10

independent trials (this would be 7 successes

out of the 10 trials) with probability 0.5 for

each trial.

To find a probability for a binomial percent using StatPads main dialog box, select

Probability as the situation and Binomial Percent as the analysis. Choose the type of probability

you want (Equal to, This or more, This or less, or Between), then give the Value(s) requested as

a percentage. Specify the Number n of trials and the Probability for each trial of the binomial

distribution. Check the Output Range, and then select Do It.

The probability that a binomial percentage


is equal to 70% is:

0.117


Binomial Percent (Between)


probability that a binomial percent is This

value or more, This value or less, or

Between two values.



percentage distribution is between 70% and

90%. That is, the probability is 0.171 of

observing between 70% and 90% successes

out of 10 independent trials with probability

0.5 for each trial (which, in this case,

corresponds to 7, 8, or 9 occurrences

representing 70%, 80%, or 90% successes).

To find a probability for a binomial percent using StatPads main dialog box, select

Probability as the situation and Binomial Percent as the analysis. Choose the type of probability

you want (Equal to, This or more, This or less, or Between), then give the Value(s) requested as

a percentage. Specify the Number n of trials and the Probability for each trial of the binomial

distribution. Check the Output Range, and then select Do It.

The probability that a binomial percentage


is between 70% and 90% is:

0.171


Poisson Probability (Equal to)

A Poisson distribution describes the

number of times an event happens, where the

event happens independently at a fixed mean

rate.


probability (0.0337) that a specified Poisson

distribution is exactly equal to 1. That is, the

probability is 0.0337 of observing exactly 1

occurrence of the event when we expect on

average to see 5 occurrences. The probability

is small because we expect many more (5

occurrences), on average, but may

occassionally (about 3% of the time) see just

one.

To find a Poisson probability using StatPads main dialog box, select Probability as the

situation and Poisson Probability as the analysis. Choose the type of probability you want

(Equal to, This or more, This or less, or Between), then specify the whole-number Value(s) and

the Mean rate of occurrence (which is not required to be a whole number) check the Output

Range, and then select Do It.

The probability that a Poisson random variable

with mean 5

is equal to 1 is:

0.0337


Poisson Probability (This or Less)


probability that a Poisson random variable is

This value or more, This value or less,

or Between two values.


probability (0.265) that the specified Poisson

distribution is 3 or less. That is, the

probability is 0.265 of observing exactly 0, 1,

2, or 3 occurrences when we expect on

average to see 5 occurrences.

To find a Poisson probability using


as the situation and Poisson Probability as


Between), then give the whole-number Value(s) requested. Specify the Mean rate of occurrence

of the Poisson distribution (which is not required to be a whole number) check the Output

Range, and then select Do It.

The probability that a Poisson random variable

with mean 5

is 3 or less is:

0.265


Exponential Probability (This or More)

The exponential distribution is a skewed

continuous distribution that is often used to

model the amount of time until a task is

completed or until an event happens. The

distribution is specified by giving its mean,

which is not required to be a whole number.


probability (0.768) that the specified

exponential distribution is 2.38 or more. That

is, the probability is 0.768 of observing 2.38

or more when we expect 9 on average.

To find an exponential probability using


as the situation and Exponential Probability as the analysis. Choose the type of probability you

want (This or more, This or less, Between, or Not between), then specify the Value(s) and the

Mean, check the Output Range, and then select Do It.

The probability that an exponential random variable

with mean 9

is 2.38 or more is:

0.768


Exponential Probability (Between)


probability that an exponential random

variable is This value or less, Between

two values, or Not between two values.


probability (0.243) that the specified

exponential distribution is between 5.2 and

10.3. That is, the probability is 0.243 of

observing a value between 5.2 and 10.3 when

we expect 9 on average.

To find an exponential probability using


as the situation and Exponential Probability

as the analysis. Choose the type of probability you want (This or more, This or less, Between, or

Not between), then specify the Value(s) and the Mean, check the Output Range, and then select

Do It.

The probability that an exponential random variable

with mean 9

is between 5.2 and 10.3 is:

0.243


Discrete Probability

A discrete probability distribution is

characterized by two lists: a list of values and

a list of probabilities (where the probabilities

must add up to 1). StatPad computes the

Expected Value (also called the Mean) as the

weighted average of the values (using

probabilities as the weights) and also

computes the standard deviation, once you

specify these two columns of numbers.

StatPads results for a situation with

three possibilities is shown below, where the

probability is 0.2 that profit is 3

($thousands), the probability is 0.5 that profit

is 5, and probability is 0.3 that profit is 8.

These are specified as two separate columns of numbers, each with its name (Profit is a

column containing 3, 5, and 8, while ProbabilityOfProfit is a column containing 0.2, 0.5, and

0.3 which properly add up to 1). We see from the results below that the expected value is $5.5

thousand and the standard deviation (measuring the risk of this situation) is $1.8 thousand for

this discrete random variable.

To compute mean and standard deviation for a discrete random variable, using StatPads

main dialog box, select Probability as the situation and Discrete Probability as the analysis.

Select one from each of the two lists (or use Add Data if your columns of numbers are in the

worksheet but are not in the lists) being sure to correctly specify which one contains the values

and which one contains the probabilities. Next check the Output Range and then select Do It.

For the discrete random variable with values in Profit

and probabilities in ProbabilityOfProfit, we have:

5.50 Mean (or expected value)

1.80 Standard Deviation


Two-Sample Analysis

Summaries



data sets. When you have two samples,

StatPad first reports summaries for each

sample separately, then gives the average

difference and the standard error of the

average difference, indicating the sampling

variability of the average difference. Note

that the two samples are assumed to have the

same measurement units (e.g., dollars).

StatPads two-sample summaries (below)

are shown for the results of a survey sent to

customers in the East and to those in the

West.

To compute summaries for two samples using StatPads main dialog box, select Two

Samples as the situation and Summaries as the analysis. Select a data set from each list (or use

Add Data if your columns of numbers are in the worksheet but are not in the lists). You may

(optionally) click on Paired to specify that the data sets have a natural pairing if the counts are

equal for the two data sets. Next check the Output Range and then select Do It.

The Paired check-box only affects the standard error of the difference. For a paired

situation, StatPad gives the ordinary standard error for the paired differences. For an unpaired

situation, StatPad uses the large-sample formula S n S n12

1 2

2

2/ / if both counts are at least 30.

Otherwise, StatPad uses the small-sample formula (assuming equal population variabilities)

( ) ( ) / / / ( )n S n S n n n n1 12

2 2

2

1 2 1 21 1 1 1 2 .

East West Summaries

17 19 Count n

1,834 2,390 Mean or average

661 761 Standard deviation (variability of individuals)

752 836 Smallest

1,295 2,004 Lower quartile

1,931 2,294 Median

2,426 2,853 Upper quartile

2,975 4,085 Largest

160 175 Standard error (variability of sample average, if random sample) 557 Average difference, West East

239 Standard error of the difference

using the small-sample unpaired formula,

which assumes equal population variabilities.


Histograms

Histograms are used to visually explore

data sets. The data axis is horizontal, and the

bars show how many data values are within

each interval. Data are concentrated where

bars are tall. You can see typical value,

variability, and distribution shape.

StatPads histograms are shown below

for the East and West survey data, one

histogram for each data set.

To create histograms for two samples

using StatPads main dialog box, select Two

Samples as the situation and Histograms as

the analysis. Select a data set from each list

(or use Add Data if your columns of numbers are in the worksheet but are not in the lists). Next

check the Output Range and then select Do It.

StatPad chooses a default bin width and landmark for the histogram bars. If you wish to

change these, use the Customize check-box found under One Sample, Histogram. Note that

Excel (not StatPad) chooses the minimum and maximum horizontal scale. These may be changed

by leaving StatPad by hitting the Esc key or selecting Cancel, then double-clicking on the axis to

find Minimum and Maximum as Axis Options.

0

1

2

3

4

0 1000 2000 3000

East

Fre

quency

0

5

10

0 1000 2000 3000 4000 5000

West

Fre

quency


Box Plots

Box plots are used to visually explore

and compare data sets; they show you a

central box defined by the quartiles, with the

median indicated within the box. In the







StatPads detailed box plots are shown

below, on the same scale, for the East and

West survey data. Note that the western

values are generally somewhat higher,

although there is considerable overlap. There are no outliers.

To create box plots for two samples using StatPads main dialog box, select Two Samples

as the situation and Box Plots as the analysis. Select a data set from each list (or use Add Data

if your columns of numbers are in the worksheet but are not in the lists). Click on Detailed box

plot if you wish outliers to be displayed separately. Next check the Output Range and then select

Do It.


either quartile.

0 1000 2000 3000 4000 5000

East (bottom), West (top)

0 1000 2000 3000 4000 5000

East (bottom), West (top)


Confidence Interval

A two-sample confidence interval for the

population mean difference includes this

unknown population mean difference with

known confidence, e.g., 95%, when random

sampling is used and normal distributions are

assumed.

StatPads 95% confidence interval

results (below) for the mean difference, West

minus East, tell you that the bounds of the

interval are 71.16 and 1,042.42.

To compute a two-sample confidence

interval using StatPads main dialog box,

select Two Samples as the situation and Confidence Interval as the analysis. Select a data set

from each list (or use Add Data if your columns of numbers are in the worksheet but are not in

the lists). You may (optionally) change the Confidence level (from the default 95%). You may

also (optionally) click on Paired to specify that the data sets have a natural pairing if the counts

are equal for the two data sets. Next check the Output Range and then select Do It.

The two-sample confidence interval is based on the standard error of the difference,

described previously under Two Sample, Summaries. If unpaired, random sampling from each of

two normal populations is assumed (also assuming equal population variabilities if the small-

sample standard error is used). If paired, random sampling from a normal population is

assumed for the differences formed from the two measurements on each unit sampled.

Confidence interval for the difference:

West East We are 95% sure that the

population mean difference is between

71.16 and 1,042.42

using the small-sample unpaired standard error,

which assumes equal population variabilities, and also

assuming random samples from normal populations.


Hypothesis Test

A two-sample hypothesis test is used to

decide, based on data, whether or not the

unobservable population means could

reasonably be equal to each other. Because

the sample averages represent (with

statistical error) their respective unknown

population means, the result is often stated in

terms of a significant (or nonsignificant)

difference between the sample averages, both

of which are known.

StatPads two-sample hypothesis test

results for the East and West survey (below)

show a significant difference between the two

regions (East and West) on average. Results

include the t value, the p value, the practical interpretation of the results, and a formal statement

of the null hypothesis being tested.

To perform a two-sample hypothesis test using StatPads main dialog box, select Two

Samples as the situation and Hypothesis Test as the analysis. Select a data set from each list (or

use Add Data if your columns of numbers are in the worksheet but are not in the lists). You may

(optionally) click on Paired to specify that the data sets have a natural pairing if the counts are

equal for the two data sets. Next check the Output Range and then select Do It.

The two-sample hypothesis test is based on the standard error of the difference, described

previously under Two Sample Summaries. If unpaired, random sampling from each of two

normal populations is assumed (also assuming equal population variabilities if the small-sample

standard error is used). If paired, random sampling from a normal population is assumed for the

differences formed from the two measurements on each unit sampled.

The p value says that, if the population means had been equal to each other, then p is the

probability of observing such a large (or larger) difference between the sample averages.

Smaller p values indicate significance because rare events are unlikely.

Hypothesis test for East and West:

t = 2.33

p = 0.026

The sample averages

1,834 and 2,390

are significantly different (p


Many-Sample Analysis

Summaries



data sets. When you have many samples,

StatPad reports summaries for each sample

separately.

StatPads many-sample summaries

(below) are shown for the quality scores of

four suppliers (defining four samples). For

example, supplier B had 35 scores listed, with

an average of 85.14.

To compute summaries for many samples

using StatPads main dialog box, select Many

Samples as the situation and Summaries as

the analysis. Select your data sets from the list (or use Add Data if your columns of numbers are

in the worksheet but are not in the list). Next check the Output Range and then select Do It.

SupplierA SupplierB SupplierC SupplierD Summaries

20 35 15 25 Count n

90.97 85.14 76.00 89.35 Mean or average

4.68 4.84 3.73 5.05 Standard deviation (variability of individuals)

82.41 74.31 71.11 75.97 Smallest

88.57 81.61 73.10 86.77 Lower quartile

90.13 84.97 75.22 88.80 Median

93.00 89.05 79.56 93.24 Upper quartile

99.63 94.61 82.44 98.54 Largest

1.05 0.82 0.96 1.01 Standard error (variability of sample average, if

random sample)


Histograms

Histograms are used to visually explore

data sets. The data axis is horizontal, and the

bars show how many data values are within

each interval. Data are concentrated where

bars are tall. You can see typical value,

variability, and distribution shape.

StatPads many-sample histograms

(below) are shown for the quality scores of

the four suppliers. Some of the horizontal

scales have been changed using Excel chart

commands (see below) because Excels

choice did not show enough detail.

To create histograms for many samples

using StatPads main dialog box, select Many Samples as the situation and Histograms as the

analysis. Select your data sets from the list (or use Add Data if your columns of numbers are in

the worksheet but are not in the list). Next check the Output Range and then select Do It.

StatPad chooses a default bin width and landmark for the histogram bars. If you wish to

change these, use the Customize check-box found under One Sample, Histogram. Note that

Excel (not StatPad) chooses the minimum and maximum horizontal scale. These may be changed

by leaving StatPad by hitting the Esc key or selecting Cancel, then double-clicking on the axis to

find Minimum and Maximum as Axis Options.

0

2

4

6

8

70 80 90 100

SupplierA

Fre

quency

0

5

10

15

70 80 90 100

SupplierB

Fre

quency

0

1

2

3

4

70 75 80 85

SupplierC

Fre

quency

0

5

10

70 80 90 100

SupplierD

Fre

quency


Box Plots

Box plots are used to visually explore

and quickly compare data sets; they show you

a central box defined by the quartiles, with

the median indicated within the box. In the







StatPads many-sample detailed box

plots (below) are shown for the quality scores

of the four suppliers, arranged on the same

scale for easy comparison. There is one box

plot for each supplier. Suppliers A and D seem to have the highest scores overall, while supplier

C has the lowest. Supplier D has a low outlier score. The horizontal scale was changed using

Excel chart commands (see below) because Excels choice did not show enough detail.

To create box plots for many samples using StatPads main dialog box, select Many

Samples as the situation and Box Plots as the analysis. Select your data sets from the list (or use

Add Data if your columns of numbers are in the worksheet but are not in the list). Click on

Detailed box plot if you wish outliers to be displayed separately. Next check the Output Range

and then select Do It.


either quartile. Note that Excel (not StatPad) chooses the minimum and maximum horizontal

scale. These may be changed by leaving StatPad by hitting the Esc key or selecting Cancel, then

double-clicking on the axis to find Minimum and Maximum as Axis Options.

70 80 90 100

bottom to top: SupplierA, SupplierB, SupplierC,

SupplierD

70 80 90 100

bottom to top: SupplierA, SupplierB, SupplierC,

SupplierD


F Test for One-Way ANOVA

The F test for one-way ANOVA (analysis

of variance) is used to decide, based on data,

whether or not the unobservable population

means could reasonably be equal to each

other. Because the sample averages represent

(with statistical error) their respective

unknown population means, the result is often

stated in terms of a

Documents

StatPad Installation and User Guide