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Homework answers / question archive / SPSS Problem Set #1 – Frequency Distribution & Descriptive Statistics We use descriptive statistics to organize and summarize data
SPSS Problem Set #1 – Frequency Distribution & Descriptive Statistics We use descriptive statistics to organize and summarize data. We can generate single numbers to summarize data (means, SDs, SEMs) or we can summarize data in a picture including all data points (histograms). Prior to running inferential statistics, it is a good idea to get “a feel” for your data (general idea of what it looks like). In doing so, you can assure that you have met at least one of the assumptions necessary to use the t-test and ANOVA. This helps in increasing statistical validity. Below are the scores from Fujiwara-sensei’s most recent exam. There are 15 men and 15 women in his Downhill Drifting 101 class. He wants to assess the performance of his students (both statistically and visually). To help him with this task, your job is to: Set up a file in SPSS for the following data and 1. Compute descriptive statistics on the overall exam scores (mean, median, SEM, variance, SD, range) 2. Create a histogram for overall midterm scores. 3. Compute descriptive statistics (same as above) for male and female scores separately 4. Create a histogram for each gender’s scores separately 5. Create a bar graph comparing the mean midterm score (with error bars: CI) for males and females 6. Fujiwara-sensei wants to place those who scored below average by half of one SD or more into intensive training bootcamp. Which students should receive extra training? Student Gender Score Student Gender Score 1 male 87 16 female 89 2 male 53 17 female 73 3 male 92 18 female 91 4 male 70 19 female 85 5 male 78 20 female 75 6 male 73 21 female 98 7 male 91 22 female 91 8 male 60 23 female 83 9 male 77 24 female 95 10 male 82 25 female 86 11 male 85 26 female 90 12 male 33 27 female 89 13 male 88 28 female 89 14 male 98 29 female 70 15 male 88 30 female 93 ON YOUR OWN: Complete steps 1-6 again for the class’s second exam: Exam 2 Student Gender Score Student Gender Score 1 male 90 16 female 77 2 male 91 17 female 73 3 male 81 18 female 70 4 male 77 19 female 85 5 male 80 20 female 75 6 male 88 21 female 98 7 male 92 22 female 88 8 male 77 23 female 83 9 male 98 24 female 81 10 male 89 25 female 86 11 male 82 26 female 82 12 male 88 27 female 89 13 male 77 28 female 89 14 male 65 29 female 89 15 male 85 30 female 69 Problem Set #2 – Bivariate Correlations Fujiwara’s Bet Fujiwara-sensei is a believer in hard work ethic and repetitive practice. His good friend, Hondakun believes that natural-born talent is the most important factor in deciding ability of competitive downhill racers. The two are at an impasse, so Fujiwara-sensei proposes a $100 wager to settle the controversy. They have decided to analyze the data for talent, repetitions of practice, and performance on the most recent downhill time-trial for the 20 students in Fujiwara-sensei’s driving class. To assess talent, Fujiwara-sensei gave each of his students a talent score based on a ride-along driving assessment on the first day of class (scored 1-100). For dedication to practice, Fujiwara sensei has a detailed log of how many practice runs each student made before their official timed trial. Performance was assessed by time to complete the downhill trial (in seconds). Your job as the unbiased arbitrator is to: 1. Find the mean, median, mode, SD, & SE for the talent, practice, and performance scores 2. Find the Pearson’s correlation coefficient r for talent and performance. How strong is it? 3. Present the talent x performance correlation visually in a scatterplot 4. Find the Pearson’s correlation coefficient r for practice and performance. How strong? 5. Present the practice x performance correlation visually in a scatterplot 6. Decide, based on comparison of the correlation coefficient r, which variable (talent or practice) is a better predictor of performance on the task. Who lost the bet? 7. If students 1-10 were male and 11-20 female, which gender performed better? Represent visually with bar graph (error bars = CI) Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Talent 92 84 77 62 90 97 74 83 91 92 87 80 68 71 95 79 82 89 99 72 Practice 5 9 2 14 12 15 23 13 9 8 15 22 7 18 0 9 11 17 27 21 Performance 138 136 158 134 132 123 130 133 130 131 128 126 142 129 156 135 130 126 119 127 On Your Own A month has passed and the data has arrived for the most recent downhill time-trial challenge (same class of students, same initial talent scores). Fujiwara-sensei is curious about whether the talent and practice scores show the same ability for predicting performance on this second trial. Using the newly collected data for practice runs and performance, complete the 7 steps once again on your own (Due 4/14): 1. Find the mean, median, mode, SD, & SE for the talent, practice, and performance scores 2. Find the Pearson’s correlation coefficient r for talent and performance. How strong is it? 3. Present the talent x performance correlation visually in a scatterplot 4. Find the Pearson’s correlation coefficient r for practice and performance. How strong? 5. Present the practice x performance correlation visually in a scatterplot 6. Decide, based on comparison of the correlation coefficient r, which variable (talent or practice) is a better predictor of performance on the task. If the bet was continued for this second time trial, who was victorious? 7. If students 1-10 were male and 11-20 female, which gender performed better? Represent visually with bar graph (error bars = CI) Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Talent 92 84 77 62 90 97 74 83 91 92 87 80 68 71 95 79 82 89 99 72 Practice 20 18 16 15 14 13 22 20 10 11 14 18 20 8 27 22 14 11 29 13 Performance 180 183 185 187 184 182 179 181 201 197 190 184 184 204 176 182 192 198 171 194 PSYC 3110 Problem Set #3 – Independent Samples t-test The faculty in the department of Psychology at a prestigious University are very concerned about the fact that many students, after passing their research method course, later go on to do poorly in their laboratory classes. Students have either reported that they simply do not remember the material or that they never really learned it in the first place. One possible explanation for the poor performance is that the range of material is too great for just one course. The faculty decided to run an experiment to determine the effectiveness of splitting the course into two conceptually similar halves (occupying one full semester). The faculty want to determine if there is any difference in learning between the two course versions, so the hypothesis is that students in the 1-course class will perform differently than students in the 2course class. Forty students were randomly selected and randomly assigned to a two-course group (n=20) or a one-course group (n=20). To determine whether there actually was a difference in student performance, the students took the same cumulative final exam at the end of the semester. Their scores are listed below. 1. What should the null hypothesis of your investigation be? What is your alpha level? 2. What are the mean scores, SD, and SE of the two groups? 3. What are the descriptive statistics for age of the two groups? 4. Represent the comparison of means in a bar chart with standard error and labels for the mean. 5. What is the t-value for the comparison between groups? 6. What is the degree of freedom (df)? 7. What is the significance of this comparison? 8. What is the confidence interval? Does it include 0? 9. Should you accept or reject the null hypothesis? 10. What is your final conclusion about the teaching of this class? (which version is better?) Student Age 1 21 2 22 3 21 4 26 5 32 6 26 7 21 8 35 9 31 10 44 11 24 12 20 13 27 14 24 15 30 16 22 17 25 18 28 19 37 20 29 Gender F F M F F F M M F F F M M F F F M M F F Group 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class 2-class Score 87 95 89 81 73 92 95 90 94 84 88 81 75 93 87 85 80 90 87 95 Student 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Age 22 21 29 21 31 24 31 22 37 38 35 21 22 26 25 23 21 22 24 41 Gender F F F F F M M M M F F F M F F F M F F M Group 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class 1-class Score 72 62 85 70 98 77 79 76 66 64 75 65 80 81 78 92 60 62 74 71 On Your Own: Fujiwara-sensei read about this class study in his favorite Psychological journal and it sparks his curiosity as to whether dividing his twice a week, 2-hour lectures into 4 per week, 1-hour lectures can affect his student scores on an upcoming exam. He hypothesizes that number of meetings will have an impact on scores, despite meeting for the same total duration of time per week. The 40 students in his class are randomly assigned to the 2-class per week and 4-class per week groups, and their average scores on the exam are listed below. 1. What should the null hypothesis of your investigation be? What is your alpha level? 2. What are the mean scores, SD, and SE of the two groups? 3. What are the descriptive statistics for age of the two groups? 4. Represent the comparison of means in a bar chart with standard error and labels for the mean. 5. What is the t-value for the comparison between groups? 6. What is the degree of freedom (df)? 7. What is the significance of this comparison? 8. What is the confidence interval? Does it include 0? 9. Should you accept or reject the null hypothesis? 10. What is your final conclusion about the teaching of this class? (which version is better?) Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Age 19 21 22 20 18 25 27 19 22 26 27 23 22 28 21 18 16 22 27 29 Gender F F M F F F M M F M F M M F M F M M F F Group 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk 2/wk Score 82 94 85 87 98 81 95 76 76 90 95 91 80 81 78 87 70 75 74 80 Student 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Age 16 31 22 26 24 27 17 18 21 27 25 19 23 21 20 52 21 19 22 26 Gender F M F F F M M F M F F F M F M F M F F M Group 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk 4/wk Score 85 95 89 78 71 92 95 83 99 84 84 81 75 93 77 85 90 90 87 91 Problem Set #4 - ANOVA Sleep researchers have theorized that, in a broad evolutionary sense, sleeping disruptions during periods of perceived environmental threat may have survival value. Previous research has shown that individuals experiencing anxiety or stress exhibit reduced periods of deep sleep and increased periods of light sleep because a person can most easily be aroused by a sound in the environment while in light sleep (Kilpatrick & Feeney, 2003). An attachment researcher conducted a study to examine the effects of anxious, avoidant and secure attachment styles on the physiology of sleep in children. The investigator hypothesized that children with anxious (and perhaps avoidant) attachment styles experience more sleep disturbances than children with secure attachment styles because they feel responsible for monitoring the external environment and regulating the distance between themselves and their parents. These children may develop patterns of light sleep because of the need to be aware of their parents’ presence at all times. Deep sleep can be experienced as threatening to attachment bond and thus dangerous to the child. The sleep patterns of 10 secure, 10 anxious and 10 avoidant 5-year-old children were monitored. Of primary importance to the attachment researcher was the overall percentage of time that each child spent in deep (delta) sleep. It was hypothesized that children who are insecurely attached to their primary caregivers will spend a lower percentage of time in deep (delta) sleep as compared to their secure counterparts. Below is the average amount of time that each child spent in delta sleep, expressed as a percentage of total sleep time. 1. What should the null hypothesis of your investigation be? What is your alpha level? 2. Within or Between groups? One-way or two-way ANOVA? Why? 3. What are the mean scores, SD, and SE of the three groups? 4. Represent the comparison of means in a bar chart with standard error, labels for the mean, and title. 5. Was Levene’s test significant? Which post-hoc test should you use? 6. What is the between groups variance (mean square)? Within groups? F value (APA format)? F value significance? 7. What is the Post Hoc significance of each comparison? 8. Should you accept or reject the null hypothesis? 9. What are your final conclusions about attachment style and sleep in children? (which children sleep better?) Child 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Attachment secure secure secure secure secure secure secure secure secure secure anxious anxious anxious anxious anxious Delta Sleep 21 21 25 23 24 23 23 22 24 22 17 17 15 15 16 Child 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Attachment anxious anxious anxious anxious anxious avoidant avoidant avoidant avoidant avoidant avoidant avoidant avoidant avoidant avoidant Delta Sleep 14 20 13 14 18 18 20 18 19 17 17 15 16 17 18 On Your Own - The same researchers are curious as to whether attachment style of children has an effect on deep sleep of their parent. The sleep patterns of 15 parents with secure children, 15 parents with anxious children, and 15 parents with avoidant children were monitored. It was hypothesized that parents of children with less secure attachment styles would have less deep sleep. Below are the data for percentage of time parents were in delta sleep. 1. What should the null hypothesis of your investigation be? 2. Within or Between groups? One-way or two-way ANOVA? 3. What are the mean scores, SD, and SE of the three groups? 4. Represent the comparison of means in a bar chart with standard error, labels for the mean, and title. 5. Was Levene’s test significant? Which post-hoc test should you use? 6. What is the between groups variance (mean square)? Within groups? f value (APA format)? f value significance? 7. What is the post-hoc significance of each comparison? 8. Should you accept or reject the null hypothesis? 9. What are your final conclusions about child attachment style and sleep in parents? (which parents sleep better?) Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Attachment secure secure secure secure secure secure secure secure secure secure secure secure secure secure secure anxious anxious anxious anxious anxious anxious anxious anxious Delta Sleep 14 20 15 14 18 16 20 18 19 17 17 15 16 17 18 14 16 13 14 13 11 15 11 Subject 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 Attachment anxious anxious anxious anxious anxious anxious anxious avoidant avoidant avoidant avoidant avoidant avoidant avoidant avoidant avoidant avoidant avoidant avoidant avoidant avoidant avoidant Delta Sleep 14 15 13 14 17 18 19 18 19 18 20 18 19 23 18 22 21 23 21 19 26 20 *Disclaimer: made up data