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Context: We are interested in examining the effectiveness of final exams in classes here at SFC. To accomplish this, we surveyed a small sample of both students (n = 50) and teachers (n = 21). The survey included a list of questions asking about people’s opinions of exams, as well as some basic background information. Assuming the sampling procedure is valid.

After collecting the data, we organized it into six columns as given in Unit5 TestData.sav. The first column lists everyone by an anonymous ID number (ID), followed by each participant’s status as a teacher or student (STAT), the language of instruction for their class (LNG), and three rating questions (Q1-Q3). The entire survey is given below:


Question 1 (5 points): The first thing we want to do is describe the data we have collected, since this will be useful in checking assumptions prior to running statistical tests.

a) Run separate descriptive data for teachers and students on each of the three survey questions and complete Table 5.1.

Table 5.1
Descriptive Data for Students (n = 50) and Teachers (n = 21)

95% CI
M Med SD Min Max SE Lower Upper
Students



Teachers




b) Look at the results for Q2 only. In one paragraph, describe the data for teachers and students individually and in comparison to one another. What can we say about these two groups based on this information? Cite specific statistical values from Table 5.1 to support your claims.


c) Before running any kind of statistical test, on which of the three survey questions (if any) do you suspect there might be a statistical difference between responses by teachers & students? Cite specific statistical values from Table 5.1 to support your claims.


Question 2 (7 points): We want to compare means for responses on Q1 in association with the language used in the class to see if group membership here impacts differences in opinions. Assume that we only have t-tests available to us to make these comparisons.

a) What specific type of t-test will be most appropriate for making these comparisons?


b) How many t-tests will we need to conduct? Please list out the specific comparisons to be made.


c) Aside from independence, what other assumptions do we need to confirm prior to running our analyses? Do our data meet these assumptions? Defend your answers citing relevant evidence.


d) Run your t-tests and complete Table 5.2. (HINT: When “defining” groups in SPSS, you have to tell it which values to compare from the dataset)

Table 5.2
Summary Statistics of Means Comparisons

t df p






e) Interpret the results of the t-tests. Write your answers in 1-2 paragraphs and cite specific statistical values from Table 5.2 to defend your claims. Be sure to also consider the context of the study and what the results mean relative to what we are analyzing.


f) Statistically, why would we not want to run t-tests in this situation? What would be a better statistical test to use?


Question 3 (7 points): Now we want to examine differences in responses based on both status (STAT) and classroom language (LNG), both separately and in combination with one another. Let’s do this for the Q3 survey data.

a) First, list out all of the null hypotheses and their corresponding alternative hypotheses for this analysis.


b) Run the appropriate analysis and complete Table 5.3. (Hint: Remember that the sum of the SS column should add up to the Total in the last row)

Table 5.3
Summary Statistics for Differences on Q3 by Status and Language

SS df MS F p Eta2 Power
STAT
LNG
STAT x LNG
Error
Total


c) We also decide to run Post Hoc tests on one of the variables. Which variable do we need these for, and why?



d) In ~2 paragraphs, interpret the results of Table 5.3, including interpretations of significance, effect size, and power, as well as the results of the appropriate Post Hoc tests. Cite specific statistical values from Table 5.3 to defend your claims. Be sure to also consider the context of the study and what the results mean relative to what we are analyzing.



Bonus (1 point): Run a similar analysis to what you did above, but this time on Q2 from the survey. You’ll note that a significant interaction effect was observed for the data.

a) Interpret what this effect means. (Hint: Make a graph of the results to help you understand it)