# 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:

- State the appropriate null and alternative hypotheses, Ho and Ha.
- 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.
- Find the p-value of the test.
- Based on the p-value, decide whether or not the results are significant and draw your conclusions in context.
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## Contents

## 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)^{[2]} found that instructor reputation has a profound impact on actual teacher ratings, and Towler and Dipboye (1998)^{[3]} 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?

- Let μ
_{1}be the mean teacher rating score for subjects in the charismatic condition and μ_{2}be the mean teacher rating score for subjects in the punitive condition. State the hypotheses that are being tested in this problem. - 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.

- Report the p-value for the statistical test.
- 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.

## References

- ↑ Open Learning Initiative.
*Statistics*. Retrieved from the Open Learning Initiative web site http://oli.web.cmu.edu/openlearning/forstudents/freecourses/statistics. - ↑ Kelley, H. H.(1950). The warm-cold variable in first impression of persons.
*Journal of Personality, 18*, 431-439. - ↑ Towler, A., & Dipboye, R. L. (1998). The effect of instructor reputation and need for cognition on student behavior (poster presented at American Psychological Society conference, May 1998)