A psychologist would like to know whether the season (autumn, winter, spring, and summer) has any consistent effect on people's sexual activity. In the middle of each season, a psychologist selects a random sample of 23 students. Each individual is given a sexual activity questionnaire. A one-factor ANOVA was used to analyze these data. Complete the following ANOVA summary table (a = 0.05). Round your answers to three decimal places, if necessary. Hint: Find the MSB, and work backwards, using the dfB. Hint: What is the relationship between SSB, SSW, and SST? df Source Between Within Total SS 58.59 X 473.44 532.03 X 3 ✓ 88 91 MS 19.53 5.38 F P-value 3.63 0.0160

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
## Analysis of Sexual Activity Across Seasons Using ANOVA

A psychologist aims to determine if the season (autumn, winter, spring, and summer) consistently affects people's sexual activity. In the middle of each season, a random sample of 23 students is surveyed using a sexual activity questionnaire. A one-factor ANOVA evaluates the collected data. Answers should be rounded to three decimal places.

### ANOVA Summary Table

| Source  | SS     | df  | MS    | F    | P-value |
|---------|--------|-----|-------|------|---------|
| Between | 58.59  | 3   | 19.53 | 3.63 | 0.0160  |
| Within  | 473.44 | 88  | 5.38  |      |         |
| Total   | 532.03 | 91  |       |      |         |

**Hints:**
- To find \( MS_B \) (Mean Square Between), work backwards using the \( df_B \) (degrees of freedom between).
- Understand the relationship between \( SS_B \) (Sum of Squares Between), \( SS_W \) (Sum of Squares Within), and \( SS_T \) (Total Sum of Squares).

### Explanation

- **Between Groups (Between)**: This represents the variance due to the interaction between the groups—seasonal effects in this case.
- **Within Groups (Within)**: Accounts for variance within each group.
- **Degrees of Freedom (df)**: Indicates the number of independent values that can vary in the analysis.
  - For Between Groups: \( df_B = 3 \)
  - For Within Groups: \( df_W = 88 \)
  - Total \( df_T = 91 \)
- **Mean Square (MS)**: SS divided by its respective df.
- **F-value**: Calculated by dividing the MS between by MS within; used to determine statistical significance.
- **P-value**: Shows the probability that the observed results occurred by chance. A P-value less than 0.05 indicates statistical significance.

This table indicates a statistically significant effect of the seasons on sexual activity, as shown by a P-value of 0.0160.
Transcribed Image Text:## Analysis of Sexual Activity Across Seasons Using ANOVA A psychologist aims to determine if the season (autumn, winter, spring, and summer) consistently affects people's sexual activity. In the middle of each season, a random sample of 23 students is surveyed using a sexual activity questionnaire. A one-factor ANOVA evaluates the collected data. Answers should be rounded to three decimal places. ### ANOVA Summary Table | Source | SS | df | MS | F | P-value | |---------|--------|-----|-------|------|---------| | Between | 58.59 | 3 | 19.53 | 3.63 | 0.0160 | | Within | 473.44 | 88 | 5.38 | | | | Total | 532.03 | 91 | | | | **Hints:** - To find \( MS_B \) (Mean Square Between), work backwards using the \( df_B \) (degrees of freedom between). - Understand the relationship between \( SS_B \) (Sum of Squares Between), \( SS_W \) (Sum of Squares Within), and \( SS_T \) (Total Sum of Squares). ### Explanation - **Between Groups (Between)**: This represents the variance due to the interaction between the groups—seasonal effects in this case. - **Within Groups (Within)**: Accounts for variance within each group. - **Degrees of Freedom (df)**: Indicates the number of independent values that can vary in the analysis. - For Between Groups: \( df_B = 3 \) - For Within Groups: \( df_W = 88 \) - Total \( df_T = 91 \) - **Mean Square (MS)**: SS divided by its respective df. - **F-value**: Calculated by dividing the MS between by MS within; used to determine statistical significance. - **P-value**: Shows the probability that the observed results occurred by chance. A P-value less than 0.05 indicates statistical significance. This table indicates a statistically significant effect of the seasons on sexual activity, as shown by a P-value of 0.0160.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman