Question

Your view on whether you view a chocolate bar as delicious or fattening may depend on your gender. In a study of American college students, Rozin, Bauer, & Catanese (2003) examined the importance of food as a source of pleasure versus concerns about food associated with weight gain and health. The following results are similar to those obtained in the study. The dependent variable is a measure of concern about the negative aspects of eating.

Male Participants. Female Participants   

n=9

n=15

Xbar (mean)=33

Xbar (mean)=42

S2=92.5

s2=88.6

Based on these results, is there a significant difference between attitudes for men and women? Use a two-tailed test with an alpha of 0.01.

Compute Cohen’s d to measure effect size. What does it tell us about the relationship?

Write a sentence demonstrating how the result of this hypothesis test and measure of effect size would appear in a research report.

Answer 1

We will use the Two-Sample t-Test for the calculation of the above problem.

A two-sample t-test is used to test the difference (d0) between two population means. A common practice is to determine whether the means are equal or not.

Hypothesis :

Null : μ1 - μ2 = d vs alternative : μ1 - μ2 ≠ d

Where μ1 =mean attitude for male population, μ2=mean attitude for the female population, d= difference of the means =0

Alpha=0.01=level of significance.

The test statistic is a t statistic (t) defined by the following equation.

t = [ (x1bar - x2bar) - d ] / sqrt[(s₁²/n1) + (s₂²/n2)]

=[(33-42)0]/sqrt[92.5²/9+88.6²/15]= -9/38.393=-0.223441

where x1bar is the mean of sample 1, x2bar is the mean of sample 2, d is the hypothesized difference between population means, s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, and n1 is the size of sample 1, and n2 is the size of sample 2

DF = (s₁​​​​​​²/n1 + s₂²/n2)2 / { [ (s₁² / n1)2 / (n1 - 1) ] + [ (s₂²/ n2)2 / (n2 - 1) ] }

=15.4636 or 15 (after rounding to nearest integer)

The t-critical values for a two-tailed test, for a significance level of alpha= 0.01 or α=0.01 isf rom table of 2 sample t distribution (2 tailed) and it is 2.947.

As observed value= - 0.223441< critical value =2.947, we accept H0 and conclude there is no significant difference among the two group means of males and females.

For the independent samples T-test, Cohen's d is determined by calculating the mean difference between your two groups, and then dividing the result by the pooled standard deviation.

Cohen's d = (M2 - M1) ⁄ SDpooled where,

SDpooled = √((SD12 + SD22) ⁄ 2)

Cohen's d = (42 - 33) ⁄ 87.689823 = 0.102634.

Cohen suggested that d=0.2 be considered a 'small' effect size, 0.5 represents a 'medium' effect size and 0.8 a 'large' effect size. This means that if two groups' means don't differ by 0.2 standard deviations or more, the difference is trivial, even if it is statistically signficant.

Hence here cohen's d=0.102634, it indicates a small effect size i.e the group means do not differ significantly which is also indicated by our 2 sample t test.

[note : An effect under 0.2 can be considered trivial, even if the results are statistically significant.]