Question

Independent Samples t-test (Worth 15 points) Scenario: An article in the journal Applied Nutritional Investigation reported the results of a comparison of two different weight-loss programs (Liao, 2007). In the study, obese participants were randomly assigned to one of two groups: (1) the soy group, a low-calorie group that ate only soy-based proteins or (2) the traditional group, a low-calorie group that received 2/3 of their protein from animal products and 1/3 from plant products. One of the dependent measures collected was the amount of body fat loss as a percentage of initial body weight. Fictional data on the percent of body fat loss appear in the table. Table: Diets Soy Diet 2.5 1.7 2.5 Traditional Diet 1.21 0.86 1.78 1.23 0.50 1.76 1.9 3.2 (a) Calculate a 95% confidence interval and assess the research hypotheses. (8 pts) (b) Compute the effect size for this study and interpret its meaning. (7 pts)

Answer 1

A)

Given the data :

x	y
2.5	1.21
1.7	0.86
2.5	1.78
1.9	1.23
2	0.5
3.2	1.76

The following results can be obtained (n: no of obs = 6) :

mean 1	2.3
mean 2	1.223333333
sd 1	0.547722558
sd 2	0.500666223
variance 1	0.3
variance 2	0.250666667
(n-1) * variance 1	1.5
(n-1) * variance 2	1.253333333
pooled variance	0.275333333
pooled sd	0.524722149

Thus t statistic is - (mean 1 - mean2 ) / [ pooled sd * sqrt(1/n +1/n)]

= (2.3 - 1.23 ) / [0.5247* sqrt(1/3)]

=3.55

Under null hypothesis the test follows t distribution with 6+6-2=10 degrees of freedom.

Critical point for2 tailed 95% for t distribution with 10 df is : 2.23

Thus observed t statistic is 3.55 > 2.23

thus based on the data it can be concluded that the null hypothesis is to be rejected, ie. the soy group and traditional group seem to have different mean effects.

The 95% confidence interval is given by - :

= sample mean difference +- upper 0.025 point for t dist with 10 df * pooled sd

=1.08 +- (2.22* 0.52)

=1.08 +- (1.15)

=(-0.07,2.23)

B)

The effect size is given by - :

Mean difference / pooled sd

= 1.08/0.52 = 2.05 which is roughly 2.

This implies that there is a large size effect roughly 2 times meaning the change in soy from traditional has had a huge effect.