Comparing means for two independent samples--teacher ratings

This activity provides independent practice in use of the independent samples t test within the context of the 4 steps of hypothesis testing:

1. State the appropriate null and alternative hypotheses, Ho and Ha.
2. Obtain a random sample, collect relevant data, and check whether the data meet the conditions under which the test can be used. If the conditions are met, summarize the data by a test statistic.
3. Find the p-value of the test.
4. Based on the p-value, decide whether or not the results are significant and draw your conclusions in context.

Research question

How powerful are rumors? Frequently, students ask friends and/or look at instructor evaluations to decide if a class is worth taking. Kelley (1950) found that instructor reputation has a profound impact on actual teacher ratings, and Towler and Dipboye (1998) replicated and extended this study, asking the question: does an instructor's prior reputation affect student ratings?

Subjects were randomly assigned to one of two conditions. Subjects in the first condition were told that they were about to watch a lecture given by a charismatic and caring lecturer. Subjects in the second condition were told that they were about to watch a lecture given by a punitive and uncaring lecturer.

Separately for each condition, subjects watched the same twenty-minute lecture given by the exact same lecturer. Following the lecture, subjects answered three questions about the leadership qualities of the lecturer. A summary rating score was computed and used as the variable "rating" here.

The resulting dataset includes 2 variables.

• Condition: the content of the description that the students were given about the professor (1 = charismatic, 2 = punitive)
• Rating: how favorably the subjects rated the professor after hearing the lecture (higher ratings are more favorable)

For the analysis, the significance level, α, is set at .01.

Dataset

Obtain the dataset from one of the following:

• class website: teacher_ratings.por (portable file format)
• ratings.xls

Analyses

The following instructions and guiding questions will step you through the analysis process. Copy and paste the following two sections into a word processor. Provide responses as indicated.

Comparing mean teacher ratings for the charismatic and punitive conditions

• What is the explanatory variable?
• What is the response variable?
1. Let μ1 be the mean teacher rating score for subjects in the charismatic condition and μ2 be the mean teacher rating score for subjects in the punitive condition. State the hypotheses that are being tested in this problem.
2. Data collection and examination
• Look at the data. Using SPSS, calculate descriptive statistics for each group and create a histogram (see instructions) for each group or side-by-side box plots. Describe the data and shape of the distributions.
• Explain why the conditions which allow us to safely use the independent samples t test are met.
• Would it be valid to use the t test if the data were somewhat skewed? Explain.
• Using SPSS, run the independent samples t test procedure (see instructions).
• Report the value of the test statistic.
• How is the t statistic calculated (write the formula)?
• Describe what this t statistic value means.
3. Report the p-value for the statistical test.
4. Interpret the analysis results in the context of the research question.
• Indicate whether or not Ho is rejected. Provide evidence.
• Draw conclusions based on the results, given the context of the research question.
• If Ho is rejected, report a confidence interval on the difference between the means of the two conditions, appropriate to the given significance level. Interpret this interval in the context of the research question.

Thought question

• Compare the one-tailed and two-tailed p-values for this test. How does choosing a one-tailed alternative impact the outcome of the study?

Resources

This activity is based on the case study "Teacher Ratings" included in Online Statistics: An Interactive Multimedia Course of Study.