Review of SPSS basics & Displaying Distributions Statistics for the Social Sciences Psychology 340 Spring 2010

Review of SPSS basics & Displaying Distributions

Statistics for the Social SciencesPsychology 340

Spring 2010

PSY 340Statistics for the

Social Sciences Announcements

• Quizzes (at least quiz 1) should appear soon– Pay attention to the due dates & times

– Don’t wait until the last min.

– Can take up to 3 times, don’t need to do them all at the same time (but only those taken by the due date/time count)


Social Sciences Types of statistics

Descriptive Statistics Used to describe summarize, simplify, and organize data

(distributions of observations) Includes: graphs, tables, measures of shape, center, and

variability Inferential Statistics

Used to test hypotheses about the population based on observations from samples

Includes things like t-tests, ANOVA, correlation & regression analyses


Social Sciences What are samples?

• Who do we test?– Population

• The set of all individuals of interest

– Sample• A subset of the population from whom data is collected

Typically we don’t have access to all of the population

We test these folks and then generalize the results to the population as a whole


Social Sciences What are samples?

– “Sample” - may also be used to refer to the participants (randomly) assigned to a particular condition of the experiment

condition A

condition B condition C

condition D

– Sample• A subset of the population from whom data is collected


Social SciencesLet’s get some data

• On a sheet of paper (that you’ll turn in) write out these pieces of information:– Male or female– Height (in inches)– How many pairs of shoes in your closet– Typical number of servings of soda per day– Typical number of servings of water per day– Which day of the week is your busiest?– On a scale of 1 (“hate it”) to 7 (“love it”) rate how you feel about

statistics


Social Sciences Basic Concepts

Variable– A condition or characteristic that can have different

values

Value– A possible number or category that a score can have

Score– A particular person’s value on a variable


Social Sciences Measurement issues

• Understand what the measurements mean– The correspondence between the way you measure the

variable and the variable (i.e., what your observations mean)

– Impacts what kind of statistics you can do, what kind of comparisons you can make


Social Sciences Scales of measurement

• Nominal Scale: Consists of a set of categories that

have different names. – Measurements on a nominal scale label and categorize

observations, but do not make any quantitative distinctions between observations.

– Example:

• Eye color:blue, green, brown, hazel



• Ordinal Scale: Consists of a set of categories that are organized in an ordered sequence. – Measurements on an ordinal scale rank observations in

terms of size or magnitude.– Example:

• T-shirt size: Small, Med, Lrg, XL, XXL



• Interval Scale: Consists of ordered categories where all of the categories are intervals of exactly the same size. – With an interval scale, equal differences between

numbers on the scale reflect equal differences in magnitude.

– Ratios of magnitudes are not meaningful.– Example:

• Fahrenheit temperature scale20º40º

“Not Twice as hot”



• Ratio scale: An interval scale with the additional feature of an absolute zero point. – With a ratio scale, ratios of numbers DO reflect ratios of

magnitude.

Ratio versus interval: Ask what a score of zero means on your scale. If it is the absence of that variable then you have a ratio scale.

SPSS doesn’t distinguish between these, collapses them into ‘scale’ measurements


Social Sciences Scales & Units of measurement

• Nominal scale

• Ordinal scale

• Interval scale

• Ratio scale

Continuous variables– Variables can take any number and can be

infinitely broken down into smaller and smaller units

– E.g., For lunch I can have

Discrete variables– Broken into a finite number of discrete categories that can’t be broken down– E.g., In my family I can have

2, or 2.5 cookies

1 kid or 2 kids, but not 2.5


Social Sciences Levels of measurement

• What kind of measurement is used for each of these variables?:– Male or female– Height (in inches)– How many pairs of shoes in your closet– Typical number of servings of soda per day– Typical number of servings of water per day– Which day of the week is your busiest?– On a scale of 1 (“hate it”) to 7 (“love it”) rate how you feel about

statistics


Social Sciences Distributions

• The distribution of a variable is a description of all of the tokens of the variable within in sample (or population if you’ve got the data)– Three basic characteristics are used to describe

distributions• Shape

– How do the observations ‘stack up’, symmetry, skew, number of peaks, etc.

• Center– Where do most of the observations fall

• Variability– How similar/dissimilar are the observations to one another


Social Sciences Distribution Example

• Get the height (in inches) distribution

– If we just look at the data in an unorganized way it is hard to get a sense of how the observations are distributed



• The distribution of a variable is a description of all of the tokens of the variable within in sample (or population if you’ve got the data)– A picture of the distribution is usually helpful

• Gives a good sense of the properties of the distribution

– Many different ways to display distribution• Frequency distribution table

• Graphs

– Also ways to describe distributions numerically


Social Sciences Frequency distribution tables

• Allow us to organize large data sets• Properties of distribution easier to “see”• Most common score, range of scores, etc.


Social SciencesSteps for Making a Frequency Table(done for the ‘likability’ variable from a previous class)

• Make a list down the page of each possible value, from highest to lowest

The values of the variable

X f % c%

7 1 2.3 100

6 1 2.3 97.8

5 9 20.5 95.5

4 14 31.8 75

3 8 18.2 43.2

2 6 13.6 25

1 5 11.4 11.4


Social SciencesSteps for Making a Frequency Table

• Go one by one through the scores, making a mark for each next to its value on the list, count up how frequently each value appears and include this in the table


The number of tokens of each variable

X f % c%

7 1 2.3 100

6 1 2.3 97.8

5 9 20.5 95.5

4 14 31.8 75

3 8 18.2 43.2

2 6 13.6 25

1 5 11.4 11.4



• Figure the percentage (or proportion) of scores for each value



N=total% = (f/N)*100

The percentage of tokens at each value

X f % c%

7 1 2.3 100

6 1 2.3 97.8

5 9 20.5 95.5

4 14 31.8 75

3 8 18.2 43.2

2 6 13.6 25

1 5 11.4 11.4



• Figure the cumulative percentage (or proportion) of scores for each value



N=total% = (f/N)*100

The percentage of tokens at each value

Cumulative percentage – percentile ranks

X f % c%

7 1 2.3 100

6 1 2.3 97.8

5 9 20.5 95.5

4 14 31.8 75

3 8 18.2 43.2

2 6 13.6 25

1 5 11.4 11.4


Social Sciences

Grouped Frequency Table(do this for height variable)

A frequency table that uses intervals (range of values) instead of single values

Create this one on the whiteboard Figure out how many intervals you want, figure out the

range of values (max-min), and create your interval size Count up the number of observations in each interval


Social Sciences Distributions (Data) in SPSS

• Let’s enter some data into SPSS.

• The nature of your data determines how you enter the data into SPSS– The nature of your variables

• Scales of measurement

– The design of a study• Are the variables independent or dependent (related)

• Does SPSS need to know certain numbers are related with one another


Social Sciences Brief review of SPSS

Two view windows:

Data view

This is where you type in all of the data

To switch between the views click on the tabs


Social Sciences Brief review of SPSS

Two view windows:

Variable view

This is where you specify the details about the variables


Social Sciences The Data View

Each row corresponds to an experimental unit(called “cases” in SPSS lingo)

So each column in the data view corresponds to a row in the variable view

Each column corresponds to a variable


Social Sciences Entering Data into SPSS

• I recommend that you start by defining your variables and their properties in the variable view

• Alternative – can enter data first, SPSS will set up the variables, but it may not get all the properties correct.


Social Sciences Variable view

Name of the variable

Type of variable: numeric, text, monetary, date, etc.


Social Sciences Categorical variables in SPSS

• SPSS ‘likes’ numbers for analyses– If you plan to analyze a variable, enter it in as a

number– If it is categorical (nominal or ordinal) you can

label the values (give SPSS names to go along with the numbers)

• This includes Levels of between groups Independent variable



• Using SPSS– Analyze Descriptive Statistics -> Frequencies– Select the variable that you want a table for and click on the arrow– Click ok

• note1 : you can also select the statistics and charts options to get more than just the Freq Dist Table

• Note2 : SPSS uses every score that appears for the variable, but leaves out those for which there were 0 instances. This can influence how you interpret the scores relative to each other.

• Note3: SPSS does not create grouped frequency tables (although it essentially does when it creates histograms, more on this later)



• Three basic characteristics are used to describe distributions– Shape

• Many different ways to display distribution– Frequency distribution table

– Graphs

– Center

– Variability


Social Sciences Shapes of Frequency Distributions

Unimodal, bimodal, and rectangular


Social Sciences Shapes of Frequency Distributions

Symmetrical and skewed distributions

Normal and kurtotic distributions


Social Sciences Frequency Graphs

Histogram Plot the

different values against the frequency of each value



Histogram by hand (create one for class height) Step 1: make a frequency distribution table (may use

grouped frequency tables) Step 2: put the values along the bottom, left to right,

lowest to highest Step 3: make a scale of frequencies along left edge Step 4: make a bar above each value with a height for

the frequency of that value



Histogram using SPSS (create one for class height) Graphs -> Legacy -> histogram Enter your variable into ‘variable’

To change interval width, double click the graph to get into the chart editor, and then double click the bottom axis. Click on ‘scale’ and change the intervals to desired widths

Note: you can also get one from the descriptive statistics frequency menu under the ‘charts’ option



Frequency polygon - essentially the same, put uses lines instead of bars


Social Sciences Displaying two variables

Bar graphs Can be used in a number of ways (including

displaying one or more variables) Best used for categorical variables

Scatterplots Best used for continuous variables


Social Sciences Bar graphs

• Plot a bar graph of men and women in the class– Graphs -> bar– Simple, click define– N-cases (the default)– Enter Gender into Category axis, click ‘okay’


Social Sciences Bar graphs

• Plot a bar graph of shoes in closet crossed with men and women– What should we plot? (and why?)

• Average number of shoes for each group?– Graphs -> bar

– Simple, click define

– Other statistic (default is ‘mean’) – enter pairs of shoes

– Enter Gender into Category axis, click ‘okay’


Social Sciences Scatterplot

• Useful for seeing the relationship between the variables– Graphs -> Legacy Dialogs– Scatter/Dot– Simple Scatter, click ‘define’– Enter your X & Y variables, click ‘okay’

• Can add a ‘fit line’ in the chart editor

• Plot a scatterplot of soda and bottled water drinking

Documents

Review of SPSS basics & Displaying Distributions Statistics for the Social Sciences Psychology 340 Spring 2010