Chapter 9Chapter 9Describing Variations in DataDescribing Variations in Data

A variable is…A variable is…

A single characteristic that can vary A single characteristic that can vary and and can be measuredcan be measured

Medical Variables:Medical Variables: Biological DifferencesBiological Differences Presence, Absence & Stage of DiseasePresence, Absence & Stage of Disease Conditions of MeasurementConditions of Measurement Techniques of MeasurementTechniques of Measurement Measurement ErrorMeasurement Error

How to Interpret DataHow to Interpret DataThe Decision FactorThe Decision Factor

Decide if data is “quantitative” or Decide if data is “quantitative” or “qualitative”“qualitative”

Identify any variable which may affect data Identify any variable which may affect data usageusage

Types of VariablesTypes of Variables

Nominal: Nominal: ““the name game”, classifying in a non-the name game”, classifying in a non-

numerical way. Ex: Male/Female; Yes/No; numerical way. Ex: Male/Female; Yes/No; A,B,AB,O A,B,AB,O (BLOOD TYPES)(BLOOD TYPES)

Each classification can be given a numerical Each classification can be given a numerical data code or point for ease of statistical data code or point for ease of statistical inference. Example: Male = 1; Female = 2.inference. Example: Male = 1; Female = 2.

Gender

1 .8 .8 .8

44 36.4 36.4 37.2

74 61.2 61.2 98.3

2 1.7 1.7 100.0

121 100.0 100.0

1.00

2.00

3.00

Total

ValidFrequency Percent Valid Percent

CumulativePercent

1.00 = Male 2.00 = Female3.00 = Unknown

Types continued…Types continued…

Dichotomous or Binary Variable:Dichotomous or Binary Variable: Variables that reflect two extreme oppositesVariables that reflect two extreme opposites

Example: Living/DeadExample: Living/Dead Dichotomous and nominal variables are also Dichotomous and nominal variables are also

called “discrete variables” because the called “discrete variables” because the categories are different from one anothercategories are different from one another

Variables, continuedVariables, continued Ordinal Variables:Ordinal Variables:

Ranked variables that follow an order.Ranked variables that follow an order. Example: Surveys that ask participants to rank Example: Surveys that ask participants to rank

answers/opinions as “very satisfied”; “satisfied” answers/opinions as “very satisfied”; “satisfied” and “not satisfied”and “not satisfied”

Continuous (Dimensional) Variables:Continuous (Dimensional) Variables: Measurements which may reflect a Measurements which may reflect a

continuous line of data.continuous line of data. Example: Height, Weight, Blood Pressure, other Example: Height, Weight, Blood Pressure, other

readings that can change regularlyreadings that can change regularly

Ratio Variables:Ratio Variables:- A continuous scale in which “0” has a meaning- A continuous scale in which “0” has a meaning

Fahrenheit/Celsius Fahrenheit/Celsius ScaleScale

Centrigrade ScaleCentrigrade Scale

Both pictures are taken from google images.com

Methods of Documenting Methods of Documenting ObservationsObservations

Frequency TableFrequency Table Consists of a x and y Consists of a x and y

axis and is used to axis and is used to show two show two characteristics that characteristics that relate to one anotherrelate to one another

X Axis = ScoresX Axis = Scores Y Axis = Frequency of Y Axis = Frequency of

each scoreeach score

Score Frequency

Below 75 4

76 - 80 14

81 - 85 2

86 - 90 8

91 - 95 5

96 - 100 1

Taken from google images

Combining DataCombining Data

The grouping of The grouping of similar values similar values together in order to together in order to simplify examination simplify examination of the dataof the data Of the two sets of birth Of the two sets of birth

weights of babies at weights of babies at Cabbage Patch Cabbage Patch Hospital which is Hospital which is easier to decipher? easier to decipher?

1-3 pounds = 101-3 pounds = 10 4-6 pounds = 454-6 pounds = 45 7-9 pounds = 257-9 pounds = 25 10-12 pounds = 1210-12 pounds = 12 13+ pounds = 813+ pounds = 8

2,11,13,14,16,12,10,7,6,8,2,2,11,13,14,16,12,10,7,6,8,2,6,1,12,11,10,9,4,7,2,9,1,86,1,12,11,10,9,4,7,2,9,1,87,2,6,1,8,7,6,5,6,3,5,2,4,17,2,6,1,8,7,6,5,6,3,5,2,4,12,132,13

Frequency DistributionFrequency Distribution

Recording observations of one variable by Recording observations of one variable by using X Axis for variable and Y Axis for the using X Axis for variable and Y Axis for the frequency of occurrencefrequency of occurrence

Look at Table 9-2 and 9-3 (pp. 142, 143)Look at Table 9-2 and 9-3 (pp. 142, 143) Which has more interpretive meaning to you?Which has more interpretive meaning to you? Why?Why?

Gaussian DistributionGaussian Distribution Also Known as Also Known as

“normal distribution”“normal distribution” Real data seldom Real data seldom

follows this slopefollows this slope The larger the data, The larger the data,

the more Gaussian or the more Gaussian or “bell shaped” it would “bell shaped” it would looklook

Images taken from google images.com

Types of Visual RepresentationTypes of Visual Representation

Histogram: A bar graph of vertical bars. The area of the Histogram: A bar graph of vertical bars. The area of the bars represent proportions of all observations that fall bars represent proportions of all observations that fall within range of the barwithin range of the bar

Frequency Polygon: This is a histogram minus the bars Frequency Polygon: This is a histogram minus the bars which are replaced by dots which are then connectedwhich are replaced by dots which are then connected

Smoking Habits

Smoke >=2 PackD

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smoke>=1 and <2

PackDay N

ow

Smoke<1PackD

ay Now

>=1 PackDay and Q

uit <3 Y

ears

>1 PackDay and Q

uit >=3 Y

ear

<=1 PackDay and Q

uit <=3 Y

ear

<=1 PackDayand Q

uit >=3 years

Never Sm

oked

Age

at L

ast B

irth

day

60

40

20

0

Histogram of Smokers

Images taken from google images.com

MeasurementsMeasurements Mode: Most commonly seen value in a group of Mode: Most commonly seen value in a group of

measurementsmeasurements Example: Example:

6 9 6 8 10 6 4 4 8 11 6 106 9 6 8 10 6 4 4 8 11 6 10 The mode is 6The mode is 6

Median: Middle observation of a data group is Median: Middle observation of a data group is derived by putting numbers in order and finding derived by putting numbers in order and finding the center number. If there are an even amount the center number. If there are an even amount of data points, take the middle two and take an of data points, take the middle two and take an average.average.

Median continued…Median continued…

Example:Example: 1 4 9 20 1 4 9 20 23 2723 27 31 48 56 58 31 48 56 58

23 + 27/2 = 2523 + 27/2 = 25 Mean: The average of a group of data Mean: The average of a group of data

points points (add all numbers then divide by the number of numbers)(add all numbers then divide by the number of numbers)

Example: Using the numbers above the Example: Using the numbers above the mean is 27.7mean is 27.7

Your Turn Your Turn (time limit: 5 minutes)(time limit: 5 minutes)

Compute the Mode, Median and Mean of Compute the Mode, Median and Mean of the following monthly glucose readings for the following monthly glucose readings for Fred:Fred:

Jan = 120Jan = 120 July = 98July = 98 Feb = 100Feb = 100 Aug = 127Aug = 127 Mar = 110Mar = 110 Sept = 134Sept = 134 April = 128April = 128 Oct = 141Oct = 141 May = 138May = 138 Nov = 128Nov = 128 June = 121June = 121 Dec = 146Dec = 146

AnswerAnswer

Mode = 128Mode = 128Median = 127.5Median = 127.5Mean = 124.5Mean = 124.5

Questions…Questions…

Homework TimeHomework Time This chapter covered a great deal, so…This chapter covered a great deal, so… Please re-read the remainder of the chapter Please re-read the remainder of the chapter

beginning with page 149 – “Problems in beginning with page 149 – “Problems in analyzing a Frequency Distribution. analyzing a Frequency Distribution.

This information is a review/continuance of what This information is a review/continuance of what we have covered tonightwe have covered tonight

Please drop me an e-mail after you have re-read this area Please drop me an e-mail after you have re-read this area and indicate if you have any further questions or if you are in and indicate if you have any further questions or if you are in complete understanding of the information.complete understanding of the information.

Any Further QuestionsAny Further Questions