Twelve people completed a difficult hand-eye coordination task twice: once in a quiet room, and once in the same room while loud rock-and-roll music was being played. The order in which subjects experienced these conditions was counterbalanced: half performed in the quiet environment first, half performed in the loud environment first. The researcher measured the number of errors committed by the participant while performing. Thus, the lower the score, the better the performance. Here are the results: Participant: 1 2 3 4 5 6 7 8 9 10 11 12 Quiet Environment: 14 21 24 16 18 20 15 20 17 16 19 12 Loud Environment: 21 22 21 19 18 25 17 18 21 24 21 15 Was there a significant difference in performance between the two treatment conditions (alpha = .05 Using these scores, carry out a t test for two related samples. Follow the steps shown below. Write the Research Problem or question that we are trying to answer in the analysis. Present the null and alternative hypothesis. Assume that the researchers will carry out a one-tailed test and that they expect the pre-intervention scores to be lower than the post intervention scores. Calculate the degrees of freedom. Use Table B to identify the critical t value for alpha set equal to .05. Present the decision rule. Calculate D . Calculate SSD. Calculate sD. Calculate the standard error, sD . Calculate the observed t ratio. Present a statistical decision. Interpret the result in the context of the research situation.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Exercise 4
Twelve people completed a difficult hand-eye coordination task twice: once in a quiet room, and once in the same room while loud rock-and-roll music was being played. The order in which subjects experienced these conditions was counterbalanced: half performed in the quiet environment first, half performed in the loud environment first. The researcher measured the number of errors committed by the participant while performing. Thus, the lower the score, the better the performance. Here are the results:
|
Participant: |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
|
Quiet Environment: |
14 |
21 |
24 |
16 |
18 |
20 |
15 |
20 |
17 |
16 |
19 |
12 |
|
Loud Environment: |
21 |
22 |
21 |
19 |
18 |
25 |
17 |
18 |
21 |
24 |
21 |
15 |
Was there a significant difference in performance between the two treatment conditions (alpha = .05
Using these scores, carry out a t test for two related samples. Follow the steps shown below.
- Write the Research Problem or question that we are trying to answer in the analysis.
- Present the null and alternative hypothesis. Assume that the researchers will carry out a one-tailed test and that they expect the pre-intervention scores to be lower than the post intervention scores.
- Calculate the degrees of freedom.
- Use Table B to identify the critical t value for alpha set equal to .05.
- Present the decision rule.
- Calculate D .
- Calculate SSD.
- Calculate sD.
- Calculate the standard error, sD .
- Calculate the observed t ratio.
- Present a statistical decision.
- Interpret the result in the context of the research situation.
Exercise 5
Each of the following studies requires a t test for one or more population means. Specify whether the appropriate t test is for one sample, two independent samples, or two related samples, and in the latter case, whether it involves repeated measures or matched pairs of different subjects.
- College women who are being treated for depression at the campus counseling center were matched for initial depression and then assigned to a drug treatment condition or a placebo control condition. At the end of the treatment period, the women take a depression test and their test scores are analyzed.
- Children who have poor social skills are selected to participate in social skills training. The researcher observes the children on the playground both before and after the social skills training. For each child, she records the number of positive peer interactions. She then analyzes the mean before-after difference.
- A researcher randomly assigns high school seniors to either an experimental group where they learn about time management or to a control group where they discuss current
events. The researcher then gathers information, for all students, on homework completion. The researcher wants to find out if the time management session is effective for improving homework completion among high school seniors. - A researcher reads that the average time that adults in the United States spend watching TV is 28 hours per week. The researcher randomly selects a sample of college students. The researcher wants to find out if college students also watch TV an average of 28 hours per week.
- A Japanese educational researcher reads that American elementary students spend an average of 21 minutes each weekday doing homework. The researcher records the time spent on homework for a sample of Japanese elementary students. The researcher wants to find out if Japanese students study more than 21 minutes each weekday.
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