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Two Groups and One Continuous Variable in Visual Editing | COMM 3362, Exams of Communication

East Carolina University (ECU)Communication

Material Type: Exam; Class: Visual Editing; Subject: Communication; University: East Carolina University; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 07/30/2009

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Two Groups and One Continuous Variable
Psychologists and others are frequently interested in the relationship between a
dichotomous variable and a continuous variable – that is they have two groups of
scores. There are many ways such a relationship can be investigated. I shall discuss
several of them here, using the data on sex, height, and weight of graduate students, in
the file SexHeightWeight.sav. For each of 49 graduate students, we have sex (female,
male), height (in inches), and weight (in pounds).
After screening the data to be sure there are no errors, I recommend preparing a
schematic plot – side by side box-and-whiskers plots. In SPSS, Analyze, Descriptive
Satistics, Explore. Scoot ‘height’ into the Dependent List and ‘sex’ into the Factor List.
In addition to numerous descriptive statistics, you get this schematic plot:
2128N =
SEX
MaleFemale
HEIGHT
76
74
72
70
68
66
64
62
60
58
The height scores for male graduate students are clearly higher than for female
graduate students, with relatively little overlap between the two distributions. The
descriptive statistics show that the two groups have similar variances and that the
within-group distributions are not badly skewed, but somewhat playtkurtic. I would not
be uncomfortable using techniques that assume normality.
Student’s T Test. This is probably the most often used procedure for testing the
null hypothesis that two population means are equal. In SPSS, Analyze, Compare
Means, Independent Samples T Test, height as test variable, sex as grouping variable,
define groups with values 1 and 2.
The output shows that the mean height for the sample of men was 5.7 inches
greater than for the women and that this difference is significant by a separate
variances t test, t(46.0) = 8.18, p < .001. A 95% confidence interval for the difference
between means runs from 4.28 inches to 7.08 inches.
When dealing with a variable for which the unit of measure is not intrinsically
meaningful, it is a good idea to present the difference in means and the confidence
interval for the difference in means in standardized units. While I don’t think that is
Dichot-Contin.doc
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Two Groups and One Continuous Variable

Psychologists and others are frequently interested in the relationship between a

dichotomous variable and a continuous variable – that is they have two groups of

scores. There are many ways such a relationship can be investigated. I shall discuss

several of them here, using the data on sex, height, and weight of graduate students, in

the file SexHeightWeight.sav. For each of 49 graduate students, we have sex (female,

male), height (in inches), and weight (in pounds).

After screening the data to be sure there are no errors, I recommend preparing a

schematic plot – side by side box-and-whiskers plots. In SPSS, Analyze, Descriptive

Satistics, Explore. Scoot ‘height’ into the Dependent List and ‘sex’ into the Factor List.

In addition to numerous descriptive statistics, you get this schematic plot:

N = 28 21 SEX Female Male HEIGHT 76 74 72 70 68 66 64 62 60 58

The height scores for male graduate students are clearly higher than for female

graduate students, with relatively little overlap between the two distributions. The

descriptive statistics show that the two groups have similar variances and that the

within-group distributions are not badly skewed, but somewhat playtkurtic. I would not

be uncomfortable using techniques that assume normality.

Student’s T Test. This is probably the most often used procedure for testing the

null hypothesis that two population means are equal. In SPSS, Analyze, Compare

Means, Independent Samples T Test, height as test variable, sex as grouping variable,

define groups with values 1 and 2.

The output shows that the mean height for the sample of men was 5.7 inches

greater than for the women and that this difference is significant by a separate

variances t test, t (46.0) = 8.18, p < .001. A 95% confidence interval for the difference

between means runs from 4.28 inches to 7.08 inches.

When dealing with a variable for which the unit of measure is not intrinsically

meaningful, it is a good idea to present the difference in means and the confidence

interval for the difference in means in standardized units. While I don’t think that is

Dichot-Contin.doc

necessary here (you probably have a pretty good idea regarding how large a difference

of 5.7 inches is), I shall for pedagogical purposes compute Hedges’ g and a confidence

interval for Cohen’s d. In doing so, I shall use a special SPSS script and the separate

variances values for t and df. See the document Confidence Intervals, Pooled and

Separate Variances T. For these data, g = 2.36 (quite a large difference) and the 95%

confidence interval for d runs from 1.61 (large) to 3.09 (even larger). We can be quite

confident that the difference in height between men and women is large.

Group Statistics 28 64.893 2.6011. 21 70.571 2.2488. sex Female Male height N Mean Std. Deviation Std. Error Mean Independent Samples Test -8.005 47 .000 -5.6786 .7094 -7.1057 -4. -8.175 45.981 .000 -5.6786 .6946 -7.0767 -4. Equal variances assumed Equal variances not assumed height t df Sig. (2-tailed) Mean Difference Std. Error Difference Lower Upper 95% Confidence Interval of the Difference t-test for Equality of Means

Wilcoxon Rank Sums Test. If we had reason not to trust the assumption that

the population data are normally distributed, we could use a procedure which makes no

such assumption, such as the Wilcoxon Rank Sums Test (which is equivalent to a

Mann-Whitney U Test). In SPSS, Analyze, Nonparametric Tests, Two Independent

Samples, height as test variable, sex as grouping variable with values 1 and 2, Exact

Test selected.

The output shows that the difference between men and women is statistically

significant. SPSS gives mean ranks. Most psychologists would prefer to report

medians. From Explore, used earlier, the medians are 64 (women) and 71 (men).

Ranks 28 15.73 440. 21 37.36 784. 49 sex Female Male Total height N Mean Rank Sum of Ranks

Variables in the Equation .931 .287 10.534 1 .001 2. -63.488 19.548 10.548 1 .001. height Constant Step 1 a B S.E. Wald df Sig. Exp(B) a. Variable(s) entered on step 1: height. Classification Tablea 26 2 92. 6 15 71.

Observed Female Male sex Overall Percentage Step 1 Female Male sex (^) Percentage Correct Predicted a. The cut value is.

Discriminant Function Analysis. This is really equivalent to the independent

samples t test, but looks different. In SPSS, Analyze, Classify, Discriminant, sex as

grouping variable, height as independent variable. Under Statistics, ask for

unstandarized function coefficients. Under Classify ask that prior probabilities be

computed from group sizes and that a summary table be displayed. In discriminant

function analysis a weighted combination of the predictor variables is used to predict

group membership. For our data, that function is DF = -27.398 + .407*height. The

correlation between this discriminant function and sex is .76 (notice that this identical to

the point-biserial r computed earlier) and is statistically significant, ^2 (1, N = 49) =

39.994, p < .001. Using this model we are able correctly to predict a person’s sex

83.7% of the time.

Canonical Discriminant Function Coefficients . -27. height (Constant)

Function Unstandardized coefficients Eigenvalues 1.363a^ 100.0 100.0. Function 1 Eigenvalue % of Variance Cumulative % Canonical Correlation First 1 canonical discriminant functions were used in the analysis. a.

Wilks' Lambda .423 39.994 1. Test of Function(s) 1 Wilks' Lambda Chi-square df Sig. Classification Resultsa 26 2 28 6 15 21 92.9 7.1 100. 28.6 71.4 100. sex Female Male Female Male Count % Original Female Male Predicted Group Membership Total a. 83.7% of original grouped cases correctly classified.

Karl L. Wuensch

East Carolina University

August, 2005