# M-5

Class

Question1

1. Independent t- test also referred to as two sample t-test is an inferential statistical test used to test whether there is a statistically significant difference between the means of two unrelated samples. This implies that to use independent t- test we need to divide the class into two different groups say group 1 and group 2, then subject each of the group to one of the lectures. That is, group 1 takes the humorous lecture and group 2 takes the non- humorous lecture. No group should take both lectures.

2. Repeated measures ANOVA also referred to as dependent t-test is an inferential statistical test used to test whether there is a statistically significant difference between means of two related samples. It is similar to t- test for related samples. Divide the sample into two groups group 1 and group 2. Allow both groups attend each lecture (humorous and non- humorous lecture). The secret here is to subject both sample groups to both conditions.

3. Matched pair test is one in which all the sampled students are exposed to the same experiment. It is known as a before and after test. Here, I would measure the blood pressure for each student before any of the lectures and label it as condition 1 then measure the BP after both lectures and label it as Condition 2 then perform a sign test for matched pairs.

QUESTION2

Reasonwhy a difference score is used in computing t-value for related tests

Incases where we have similar units being subjected to bothexperiments, it is believed that any divergence in the results is dueto the difference in experiment effects rather than any other factor.This means that in related sample tests both groups are observed tobe highly correlated. Those who are lower on the dependent variablein one condition will be lower on the dependent variable in the othercondition and vice versa. Although the average score may vary in bothgroups the distribution of results in both groups should beidentical.

Question3

Theprocedure for finding the test value involves several steps:

Step1: state the hypothesis

HO:The means of the related populations are equal µ1= µ2

HA:The means of the related populations is not equal. At least one ofthe averages is different µ1≠ µ2

Step2: Find the mean of the differences between observations ()

Where= and n is the number of data pairs

 Group 1 Group 2 D =G1 – G2 D2 15 10 5 25 15 12 3 9 12 8 4 16 19 18 1 1 17 15 2 4 Total= 15 Total= 55

== = 3

Step3: Obtain the standard deviation SDof the differences using the formulae

SD= = = == 1.581

Step4: Find the estimated error =

== = 0.707

Step5: Find the test value using the formula

t= where degrees of freedom is n-1

t= = = 4.243 this is the calculated t- value

Step6: Decision making given that the level of significance (= 0.05

Fromthe t- tables obtain t- critical at =0.05. The alternative hypothesis is not directional and thereforethis is a 2-tail test. The value of t- critical is 2.78. Comparet-calculated and t-critical. If t-calculated is greater than t-critical we reject the null hypothesis at 5% level of significanceand vice versa.

Inour case t-calculated (4.243) t- critical (2.78) we reject the null hypothesis at=0.05 and conclude that the difference between the two populationmeans is significantly different from zero or simply there is astatisticallysignificant difference between the two populations’ means.

Question4

Cohen’sd effect size is a quantitative statistical measure of strengthbetween 2 factors such as the mean difference.

Calculationof Cohen’s effect size

d== =1.898 this is a huge effect size for the difference between means ofthe two samples

Question5

ConfidenceInterval is a specific range of values within which measurements (inour case the population means) falls corresponding to a givenprobability. For instance, 95% confident interval implies that we are95% certain that the difference between populations mean will lie ingroup 1 or 2.

Confidenceinterval for the mean difference

32.780.707) (2.780.707)

31.96531.965

1.0354.197

Weare 95% confident that the difference between population means is1.035 and 4.197