# Relationship of T-test and Effect Size

Can you explain the data what are the assumptions of correlated groups t test provided?

1.What are the assumptions of a correlated groups t test?

2.What measure of effect size is used for a correlated-groups t test?

3.The student decides to conduct the same study using a within-participants design in order to control for differences in cognitive ability. He selects a random sample of participants and has them study different material of equal difficulty in both the music and no music conditions. The data appear below. As before, they are measured on an interval ratio scale and are normally distributed.

Music

6, 7, 6, 5, 6, 8, 8

No music

10, 7, 8, 7, 7, 9, 8

A what statistical test should be used to analyze these data?

B Identify Ho and Ha for this study

C Conduct the appropriate analysis

D Should Ho be rejected? What should the researcher conduct

e. If significant, compute the effect size and interpret

f. If significant, draw a graph representing the data.

4. The formula is N-1 instead of N+N-2 where N is the number of participants in one group or in one sample. The way the null hypothesis is stated is also different.

Also, one advantage of the correlated-groups t test over the independent-groups t-test is that is reduces the error variance due to individual differences.

Which one do you prefer?

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#### Solution Summary

The solution gives detailed steps on solving a couple of statistical questions on t-test for two independent sampes and two dependent sampes and effect size.

T Statistics

1. indicate whether the factor influence the numerator or denominator of the t statistic and determine whether the effect would be to increase the value of t or decrease the value of t if all other factors rmain constant.

a) increase the variability of the scores

b) increase the number of scores in the sample

c) increase the difference between the sample mean and the population mean

2. What is the relationship between the value for degrees of freedom and the shape of the t distribution? What happens to the critical value of t for a particular alpha level when df increases in value?

3. the following sample was obtained from a population with unknown parameters; Scores: 1, 5, 1, 1

a) compute the sample mean and the standard deviation.

b) compute the estimated standard error for M

4. a sample of n=36 freshmen participated in a training program to prepare for a English Language skills course that all freshman have to take. The mean score for the entire freshman class was μ= 74, M= 79.4 with a standard deviation of s=18.

a) can the college conclude that the students in the new program performed signficantly better thatn the rest of the freshman? Use a one-tailed test with α= .05

b) can the college conclude that the students in the new program ar signifcantly different from the rest of the freshman class? Use a two-tailed tes with α= .05

5. a sample of n=36 adults took the supplement ginkgo biloba for 30 days. μ= 15, the individuals in the sample mean score of M= 16.9 with SS= 1260.

a) are these data sufficient to conclude that the herb has a statistically significant effect using a two-tailed tes with α= .05

b) what decision would be made if the researcher used a one-tailed test with α= .05

6. laboratory rats eat an average of μ= 21 grams of food each day. a random sample of n=100 rats where placed in a maintained humidity room of 90%. The daily consumption for the sample averages M= 18.7, with SS= 2475

a) can the researcher conclude that humidity has a significant effect on eating behavior? use a two-tailed test with α= .05

b)compute the estimated d and r² to measure the size of the treatment effect.