Comparing Two Means (t-Tests)

Practice Lab

Background

Dr. Putulowski is a business professor who applies established marketing theories to previously unstudied industries. In a recent study, Dr. Putulowski applies the "4 Ps of Marketing" (Place, Product, Promotion and Price) to the mental healthcare industry. The purpose of his research is to help psychotherapists in private practice more effectively market their businesses. In this study, Dr. Putulowski wants to know if the amount people are willing to pay for a child therapist differs depending on whether the therapist is a specialist or non-specialist. He suspects that clients will pay more if the therapist is a specialist because they have more professional training. However, it is also possible that potential clients will fail to recognize the potential benefits that a specialist offers.

In order to answer this research question, Dr. Putulowski constructs an online survey-based experiment. He recruits 107 adult college students between the ages of 19 and 53 to participate in the study. In this experiment, participants are asked to imagine that they are the parent of a child who is experiencing severe mental health problems. Next, participants are randomly assigned to one of two conditions: a specialist condition (n = 60) or a non-specialist condition (n = 47). In the non-specialist condition, they read an advertisement for a therapist in their area who has 10 years of experience. In the specialist condition, they read an identical advertisement except that the therapist is also a Registered Play Therapist who has extensive training in specialized play therapy practices. Finally, the participants are asked, "Suppose that the average cost for a therapist in your area is $100 per session. How much would you be willing to pay for this therapist's services?"

In this lab, we will determine whether the amount people are willing to pay for a child therapist differs depending on whether the therapist is a specialist or non-specialist. To complete this lab, download and open the data file called Therapy_Specialist.savwithin SPSS.

Analytic Method

First, we must determine which statistical test is most appropriate for these data. Be sure to consider the levels of measurement of the independent and dependent variables.

1. Which statistical test is most appropriate for analyzing these data?

2. Why is this statistical test appropriate?

Hypotheses

Next, we must state our null and alternate hypotheses both informally and formally.

3. What is the informal null hypothesis?

4. What is the formal null hypothesis?

5. What is the informal alternate hypothesis?

6. What is the formal alternate hypothesis?

Testing Assumptions Using Descriptive Statistics

There are several key assumptions that must be met in order for the results of our statistical test to be trustworthy.

7. What are the assumptions of this statistical test?

Normality. In order to test the assumption of normality, we will generate a descriptive statistics table of the price people are willing to pay broken down by treatment group (specialist condition vs. non-specialist condition). To do this, click Analyze Compare Means Means to open up the Means dialogue box. Select "Price Willing to Pay for Therapy" from the variables list and move it to the Dependent List box on the upper right. Then select "Type of Therapist (Specialist vs. Non-specialist)" and move it to the Independent List box on the lower right. Then click Options. Select "Kurtosis" and "Skewness" from the Statistics window and move them into the Cell Statistics box on the right. Click Continue. Then click OK. This should produce two tables in the Output Window. Copy and paste the "Report" table below:

[paste SPSS output here]

8. Examine the skewness and kurtosis statistics for the non-specialist condition. Is the assumption of normality supported?

9. Examine the skewness and kurtosis statistics for the specialist condition. Is the assumption of normality supported?

Absence of Outliers. Next, we will visually inspect the distribution of each group for outliers using a boxplot. To do this, Click Graphs Chart Builder. Next, click on Boxplot under the Gallery tab on the bottom left. Drag the first image in the gallery to the Drop zone on the top right. Select the independent variable from the variable list and drag it to the x-axis in the Drop zone. Next, select the dependent variable from the variable list and drag it to the y-axis in the Drop zone. Click OK. This should produce a graph in the Output Window. Copy and paste the bar graph below:

[paste SPSS output here]

10. Examine the distribution of the non-specialist condition. Based on visual inspection of the boxplot, are there any potential outliers?

11. Examine the distribution of the specialist condition. Based on visual inspection of the boxplot, are there any potential outliers?

Homogeneity of variance.In order to test the assumption of homogeneity of variance, we will have to run the t-test. To do this, click Analyze Compare Means Independent-Samples T Test... Move the independent variable to the Grouping Variable box. Click Define Groups... Type "1" into the Group 1 box and type "2" into the Group 2 box. Click Continue. Move the dependent variable to the Test Variable(s) box. Click OK. This should produce two tables. Paste the "Independent Samples Test" table into the document below:

[paste SPSS output here]

12. Examine the results of Levene's test for equality of variances. Is the assumption of homogeneity of variance supported?

Interpreting the Test Statistics

Once the assumptions have been met, we can interpret the results of our statistical test. We must be sure to interpret the correct test statistic on the table.

13. Examine the Independent Samples Test table that you created. Which test statistic should we interpret and why?

14. Is the difference between the two groups statistically significant? How do you know?

Calculating and Interpreting Effect Size

Next, we will determine the practical significance of our findings. To do this, we must calculate the effect size of the difference between the two means using Cohen's d using the following formula:

But we will first have to calculate the pooled standard deviation for the two groups using this formula:

Look back at the descriptive statistics table above to find the standard deviations of the two groups. Plug those values into the formula to calculate the pooled standard deviation.

15. What is the pooled standard deviation of the two groups?

Look back at the descriptive statistics table above to find the means of the two groups. Plug those values, along with the pooled standard deviation, into the formula for Cohen's d to calculate the effect size.

16. What is the effect size of the difference between the two groups? (Report the absolute value.)

Cohen suggested that d = .20 be considered a "small" effect size, .50 be considered a "medium" effect size, and .80 be considered a "large" effect size.

17. Based on Cohen's criteria, how large is the observed effect? Is it practically significant?

Reporting the Results

Now that our analyses are completed, we can formally report the results of our analysis.

18. Report the results of your analysis. Be sure to provide the key information to your readers using proper APA style.

Discussing the Results

Finally, we will discuss our results in light of our original research question and address the practical implications of our findings.

19. Based on these results, does the amount people are willing to pay for a child therapist differ depending on whether the therapist is a specialist or non-specialist?

20. What advice would you give to a child therapist in private practice who is trying to set a price for her services?