Question

a) A psychologist is interested in whether or not handedness is related to gender. Specifically, she wants to know if the percentage left-handed men in the population is different from the percentage of left-handed women. She collected data on handedness for 200 men and 200 women. What type of statistical test would be appropriate?

options: a) Chi-square goodness of fit test b) Independent samples t-test c) Paired t-test d) Chi-square test of independence

b) Nima investigated the relationship between optimism and exercise habits on recall for health information. Participants took the Life Orientation Test and were divided into low optimism and high optimism groups. These two groups were further subdivided by whether the participant rarely exercised, sometimes exercised, or frequently exercised. Each participant was presented with a page of 30 facts about healthy living, and one week later their memory for these facts was tested. Which statistical test you would use to answer the research question and/or analyze the data described?

options: a)chi-square test of independence b)repeated measures ANOVA c)one-way ANOVA d)factorial ANOVA

c) Under what circumstances will be the absolute value of the t-statistic the largest?

options: a) Small differences between means, small sample size b) Big differences between means, small sample size c) Big differences between means, large sample size d)Small differences between means, large sample size

d) Bonferroni, Holm, Tukey are all examples of (can be multiple of the following options

options 1) statistical distribution 2) inference tests 3) ANOVA terminology for variability 4)corrections for multiple comparisons

please provide the solutions and an explanation!

Answer 1

a) Answer is (d) Chi square test of independence

Note : Chi square test of independence is used to test if there is relationship between two categorical variables .Here we want to test whether two categorical variables handedness and gender are related to each other . Thus we use Chi square test of independence.

Note : Handedness is a categorical variable as it does not take quatitative values , it takes values by names : right and left. Similarly , gender is also categorical variable.

b) Answer is (b) factorial ANOVA

Note : As we want to test the effect of two independent variables( optimism and exercise habits) on the dependent variable ( recall on health information) . The independent variables are further subdivided into diiferent groups , here optimism is dividede into two groups : high and low . Similarly excesise habits is further subdivided into three groups .Then F test is done to comapre the means of these groups. This is factorial ANOVA .

c) Answer is (c) big difference bbetween means , large sample size

Note : t statistic is given by

Absolute value of t is bigger when the numerator is bigger that is big diffrence between means . Also absolute value of t is bigger when the denominator is smaller and denominator will be smaller when n is large .

d) Answer is

c) ANOVA terminology for variability

d) corrections for multiple comparison

Note : These are used in post hoc ANOVA tests . Bonferroni is used in multiple comparison tests to reduce the significant levels , so that probability of getting significant results decreases. Bonferroni holms is better than Bonferroni corrections, as power of the test gets bigger. An ANOVA test can tell us whether the difference between means are significant, but cannot tell which group is significantly different. For this we do post hoc test , Tukey test .