Statistics Problem

Question

A researcher is interested in increasing feelings of self-confidence in adolescents. He randomly selects 100 adolescents from the population and randomly assigns 50 individuals to a treatment program designed to increase self-confidence. The other 50 individuals receive no treatment program. After two weeks the 100 adolescents are measured on their self-confidence. The scale is a 20 point scale (1 = low, 20 = high self-confidence) measured on the interval level. The summary statistics for each group are as follows:

Treatment           Control
Mean 13.80           12.40
Std. Dev. 2.99        3.40
n 50                        50


a. Assuming ?=.05, two-tailed, state the cutoff score for the test.

 

 

b. Calculate the value of the standard error of the test statistic

 

 

c. What is the value of the test statistic for these data?

 

 

e. Statistical decision and interpretation 

 

f. What is the value of the effect size for these data?

 

g. What is the estimate of statistical power based on these data?

 

 

Answer 1

Christopher:

 

 

CAUTION:  You are applying a t-test (meant for normal populations) tor DISCRETE DATA!!!  Your conclusions may not be valid at all.

 

a. Assuming ?=.05, two-tailed, state the cutoff score for the test.  Answer 2.009

 

From tables of critical values of t   http://bcs.whfreeman.com/ips6e/content/cat_050/ips6e_table-d.pdf

 

b. Standard error of the test statistic  The test statistic is t.  Its variance is 48/46. The std error is 1.02.  Probably the question meant "standard error of the difference between the sample means".  If so, ask me by posting a comment.

 

c. What is the value of the test statistic for these data?  t = 2.1864

 

Use          http://www.graphpad.com/quickcalcs/ttest2/

 

 

WHAT HAPPENED TO d?

 

e. Statistical decision and interpretation

 

The P_value is 0.0312.  The data has sufficient evidence at the given 5% level of significance against the the null hypothesis that the population means of subjects receiving treatment and those receiving no treatment.

 

 

f. What is the value of the effect size for these data?  The un-standardized effect size is 13.8 - 12.4 = 1.4.

 

g.  No time right now.  Sorry.  May be later.

 

Dr. G.