Question

1. Below are several research scenarios. Indicate which set of statistical analyses should be used to analyze the data collected in study, and explain why that statistical test should be used

(a) Teachers at a local middle school were interested in exploring the effects of a collaborative peer teaching program on the motivation levels of seventh-grade students. Four of eight classes of seventh grade students were randomly selected at Bulloch Middle School to serve as subjects in this study. Students within each class were then randomly assigned to one of three groups: a collaborative peer teaching program, group learning activities, or individual learning activities. Each class was taught by a different teacher. The Middleman motivation scale was used to measure motivation in the subjects, and this scale produces scores that range from 1 to 25 with higher scores indicating greater motivation. Validity for the Middleman scale was previously ascertained by examining how scores from the Middleman motivation scale corresponded to scores from variables that are theoretically related to motivation, such as effort to achieve, persistence, intelligence, and self-efficacy. Internal consistency for scores from the Middleman scale typically range between .81 and .86. Data for the current study were collected at the end of a 16 week program. Analysis of these data revealed that students in the individual learning activities demonstrated a statistically higher level of motivation compared with students in the two other, traditional groups .

Answer 1

1.

(a)

More than two groups (three here) were formed to collect data about different methods of teaching. So, we have to perform ANOVA to perform statistical analysis.

In this hypothesis testing process, we take null hypothesis assuming that mean scores are equal in all (three here) groups. We test whether there is significant evidence to reject our null hypothesis or not. If our null hypothesis is rejected we get a conclusion that the mean scores of different groups are significantly different. In such scenario, we have to perform repeated t-test comprising of two groups of samples. As there are 3 groups we have to perform 3 t-tests with groups as follows.

• collaborative peer teaching program and group learning activities,
• collaborative peer teaching program and individual learning activities,
• group learning activities and individual learning activities.

Here it is given that analysis of these data revealed that students in the individual learning activities demonstrated a statistically higher level of motivation compared with students in the two other traditional groups. Thus to prove significant evidence of higher level of motivation in the individual learning activities, we have to perform 2 t-tests one between collaborative peer teaching program and group learning activities and another between group learning activities and individual learning activities.

So our tests are as follows.

1. ANOVA with null against alternative
2. t-test with null against alternative
3. t-test with null against alternative