Multivariate Descriptive ResearchCategorical VariablesPowerPoint PresentationSlide 4Slide 5BargraphBargraph: More than two categorical variablesBoth variables are categoricalSlide 9Slide 10Slide 11Slide 12Multivariate Descriptive Research•In the previous lecture, we discussed ways to quantify the relationship between two variables when those variables are continuous.•What do we do when one or more of the variables is categorical?Categorical Variables•Fortunately, this situation is much easier to deal with because we can use the same techniques that we’ve discussed already.•Let’s consider a situation in which we are interested in how one continuous variable varies as a function of a categorical variable.•Example: How does mood vary as a function of sex (male vs. female)?•In this case, we want to know how the average woman’s score compares to that of the average man’s score.•level of a categorical variableParticipants Mood scoreMales A 4 B 3 C 4 D 3M = 3.5, SD = .5 Females A 5 B 4 C 5 D 4M = 4.5 , SD = .5First, find the average score for each level of the categorical variable separately. (Also find the SD.)Second, find the difference between the means of each group. This is called a mean difference. (4.5 – 3.5 = 1.0)Third, express this mean difference relative to the SD. This is called a standardized mean difference.1/.5 = 2In this example, women score 2 SD higher than the men.Participants Mood scoreMales A 4 B 3 C 4 D 3M = 3.5, SD = .5 Females A 5 B 4 C 5 D 3M = 4.25 , SD = .83Note: If the SD’s for the two groups are different, you can simply average the two SD’s.Here, the two SD’s are .5 and .83. Averaged, these are (.5 + .83)/2 = .66.The standardized mean difference is (4.25 – 3.5)/.66 = .75/.66 = 1.13Thus, on average, women score 1.13 SD’s higher than men on this mood variable.Bargraph11.522.533.544.55Men WomenSexMoodBargraph: More than two categorical variables1234567Men WomenSexMoodNon-bereaved BereavedBoth variables are categorical•When two variables are categorical, it is sometimes most useful to express the data as percentages.•Example: Let’s assume that depression is a categorical variable, such that some people are depressed and others are not.•What is the relationship between biological sex and depression?Depression statusSex Not Depressed Depressed row totalMale 600 60 660Female 40 300 340column total 640 360 1000Depression statusSex Not Depressed Depressed row totalMale .60 .06 .66Female .04 .30 .34column total .64 .36 1.00In this table, we’ve expressed each cell as a proportion of the total.Depression statusSex Not Depressed Depressed row totalMale .60 .06 .66Female .04 .30 .34column total .64 .36 1.00.60/.64 = .94 .06/.36 = .16Here, we’ve expressed the association with respect to sex. For example, we can see here that 16% of people who are depressed are male. Moreover, 94% of people who are not depressed are male.Depression statusSex Not DepressedDepressed row totalMale .60 .06 .66 .06/.66 = .09Female .04 .30 .34 .30/.34 = .88column total .64 .36 1.00Here, we’ve expressed the association with respect to depression status. For example, we can see here that 9% of men are depressed and 88% of women are
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