Analysis B 1
Running head: DATA ANALYSIS: PROGRAM B
Data Analysis: Program B
J. Michael Dillon
Walden University
Research Seminar III: Quantitative Research in Education
EDUC-8438-003
Dr. Gerald Giraud, Facilitator
7-27-08
Week 8
Analysis B 1
Data Analysis: Program B
Hypothesis testing is a major part of inferential statistics. The techniques associated with hypothesis testing allow researchers to use data and statistical analysis to produce evidence the either supports or rejects a given claim. These types of conjectures can range from questions about means and proportions in a sample to comparisons between treatment and control groups. The following exercises utilize SPSS software to answer questions involving t-tests in variety of different scenarios.
One-Sample t-Test (page 160)
John is interested in determining if a new teaching method, the Involvement Technique, is effective in teaching algebra to first graders. John randomly samples six first graders from all first graders within the Lawrence City School System and individually teaches them algebra with the new method. Next, the pupils complete an eight-item algebra test. Each item describes a problem and presents four possible answers to the problem. The scores on each item are 1 or 0 where 1 indicates a correct response, and 0 indicates a wrong response. The SPSS data file contains six cases, each with eight item scores for the algebra test.
Exercise 1: Compute total scores for the algebra test from the item scores. A one-sample t test will be computed on the total scores.
Student / A / B / C / D / E / FTotal Score / 8 / 6 / 5 / 7 / 4 / 6
Exercise 2: What is the test value for this problem?
Each question has four possible choices. If a student were to randomly guess, he or she would have one in four chance of getting the answer correct. Therefore, the test value for this scenario would be 2 (0.25 ´ 8 = 2) since this score would be expected based solely on chance.
Exercise 3: Conduct a one-sample t test on the total scores. On the output, identify the following:
a) Mean algebra score b) t-test value c) p value
Output from SPSS à
a) The mean of the total test scores is 6.000
b) The t-test value is 6.928.
c) The p-value is 0.001
Exercise 4: Given the results of the children’s performance on the test, what should John conclude? Write a results section based on your analyses.
A one-sample t test was conducted on the total scores of the eight-item algebra test to evaluate whether their mean was significantly different from 2, the score that would be expected based solely on chance (random guessing between 4 possible answers). The sample mean of 6.00 (SD = 1.41) was significantly different from 2, t(5) = 6.928, p = 0.001. The 95% confidence interval for the total score mean ranged from 4.52 to 7.48. The effect size of d of 2.83 indicates a large effect from the treatment. The results of the test support the conclusion that the Involvement Technique was successful in helping the first-grade students learn algebra.
Paired-Samples t-Test (page 166)
Kristy is interested in investigating whether husbands and wives who are having infertility problems feel equally anxious. She obtains the cooperation of 24 infertile couples. She then administers the Infertility Anxiety Measure (IAM) to both the husbands and the wives. Her SPSS data file contains 24 cases, one for each husband-wife pair, and two variables, the IAM scores for the husbands and the IAM score for the wives.
Exercise 6: Conduct a paired-samples t test on these data. On the output, identify the following:
a) mean IAM (husbands)
b) mean IAM (wives)
c) t test value
d) p-value
Output from SPSS à
a) The mean IAM scores for husbands is 57.46.
b) The mean IAM scores for wives is 62.54.
c) The t test value is –3.256.
d) The p value is 0.003.
Exercise 7: Write a Results section in APA style based on your output.
A paired-samples t test was conducted to evaluate if husbands or wives who are infertile experience the same level of anxiety. The results indicated that the mean IAM score (an anxiety measure) for women (M = 62.54, SD = 12,44) was significantly greater than the mean IAM score for men (M = 57.46, SD = 7.34), t(23) = –3.256, p 0.01. The standardized effect size index, d, was 0.66, with considerable overlap in the distribution for the IAM scores for husbands and wives, as shown in Figure 1. The 95% confidence interval for the mean difference between the two ratings was –8.31 to –1.85.
Figure 1. Boxplots of IAM scores for husbands and wives.
Independent-Samples t-Test (page 173)
Billie wishes to test the hypothesis that overweight individuals tend to eat faster than normal weight individuals. To test this hypothesis, she has two assistants sit in a McDonald’s restaurant and identify individuals who order the Big Mac special (Big Mac, large fries, and large Coke) for lunch. The Big Mackers, as they are affectionately called by the assistants, are classified as overweight, normal weight, or neither overweight nor normal weight. The assistants identify 10 overweight and 30 normal weight Big Mackers. The assistants record the amount of time it takes for the individuals to complete their Big Mac special meals. The SPSS data file contains two variables, a grouping variable with two levels, overweight (= 1) and normal weight (= 2), and time in seconds to eat the meal.
Exercise 1: Compute an independent-samples t test on these data. Report the t-values and the p values assuming equal population variances and not assuming equal population variances.
For purposes of the SPSS calculations, the individuals identified as overweight were considered to be group 1 and the individuals identified as normal weight were considered to be group 2. The negative values for the t test value result from the fact that group 1 had smaller times. For assumption of equal population variances, the t test value is: –3.975 and the p-value = 0.000. If it is not assumed that there are equal population variances, the t test value is –5.397 and the p-value = 0.000.
Exercise 2: On the output, identify the following:
a) Mean eating time for overweight individuals
b) Standard deviation for normal weight individuals
c) Results for the test evaluating homogeneity of variances
Output from SPSS à
a) The mean eating time overweight individuals is 589.00.
b) The standard deviation for normal weight individuals is 82.949.
c) The results for the test evaluating homogeneity of variances are: F = 2.745 and p = 0.106
Exercise 3: Compute an effect size that describes the magnitude of the relationship between weight and the speed of eating Big Mac meals.
Since both the sample sizes are the variances are different, use the t test value from the calculation where equal variances are not assumed. To calculate the effect size, use the following process:
The effect size would be considered to be larger (greater than 0.8).
Exercise 5: If you did not include a graph in your Results section, create a graph in APA format that shows the differences between the two groups.
Figure 2. Error bars for time spent eating Big Mac meals for each weight group.
Requirement for Each Test
The following table outlines the requirements for each type of t test and provides example of situations where the test could be applied:
Test / Requirements(referenced from Green and Salkind) / Example
One-Sample
t-Test / · Variables must come from a normally distributed population
· Randomly sampled
· Each value must be independent / An example where a one-sample t-test might be used would be to test the assumption that a group of students who receive additional instruction score above average on the math portion of the ITED (Iowa Test of Educational Development) test. In this case, the mean of the group of student is being compared to population mean.
Paired-Samples
t-Test / · The scores for the differences between the means must come from a normally distributed population
· Randomly sampled
· Each difference value must be independent / An example of a situation where a paired-samples t-test would be used is if students were asked to complete a survey regarding their attitudes about mathematics before and after a new teaching technique is implemented to improve math instruction for a given unit. It is a paired-samples situation because data is collected from each student twice and these data are compared.
Independent-Samples
t-Test / · The variable must be normally distributed in each sample
· Randomly sampled
· An assumption about the variances for each sample must be made (differences can result if the variances are equal versus if they are not equal / An example of an independent-samples t-test would be to compare data between two separate groups where one group receives additional instruction beyond the normal amount prior to a calculus test and a control group receives just the normal amount.
References
Green, S. B., & Salkind, N. J. (2005). Using SPSS for Windows and Macintosh: Analyzing and understanding data (4th ed.). Upper Saddle River, NJ: Pearson Prentice-Hall.