Question

Variables and Scales of Measurement

The PHLS survey contained seven questions to measure stress. Each participant completed these seven questions:

1. • I found it hard to wind down
   • I tended to over-react to situations
   • I felt that I was using a lot of nervous energy
   • I found myself getting agitated
   • I found it difficult to relax
   • I was intolerant of anything that kept me from getting on with what I was doing
   • I felt that I was rather touchy

You were encouraged to pick a response. These responses were placed on a scale from 1 – 4. Your options were:

None of the time	Some of the time	A good part of the time	Most of the time
1	2	3	4

1. Which scale of measurement was used when measuring stress?

Nominal Ordinal Ratio Interval

2. Daily screen time was measured in minutes (e.g. 30 minutes, 60 minutes, 480 minute). Which scale of measurement was used to measure daily screen time?

Nominal Ordinal Ratio Interval

3. Employment was measured by selecting either “employed” or “unemployed”. Which scale of measurement was used to measure employment?

Nominal Ordinal Ratio Interval

4. Is employment a categorical variable?

Yes No I don’t know

5. One of the predictions for this project is that the amount of time an individual spends looking at screens the higher their stress level. In this prediction, what is the independent variable and what is the dependent variable?
   1. Independent Variable:
   2. Dependent Variable:

6. One of the predictions for this project is that unemployment influences stress. Which type of statistical analysis would you use to analyze this prediction?

t-test ANOVA Correlation Regression

7. Calculate the mean, median, and mode for each line of data below. Show your work.

Q1	Q2	Q3	Q4	Q5	Q6	Q7	Mean	Median	Mode
3	3	2	2	2	3	2	2.4	2	2
2	1	2	1	1	3	3
2	3	3	3	3	2	3
2	3	3	3	3	2	3

One-Way ANOVA

8. You are interested in how different types of exercise influence stress level and depression. On the PHLS 451 Survey, you asked which type of exercise people engage in the most. You also measured stress and depression using two different scales.

Since you are interested in two different dependent variables (i.e. stress and depression), you decide to run two, One-Way ANOVA’s. Below are the results of both One-Way ANOVA’s.

1. Write your alternative and null hypotheses for the One-Way ANOVA analyzing the relationship between exercise time and stress:

2. Looking at the ANOVA table above. Fill in the blanks below.

Looking at the results of the One-Way ANOVA, our p-value is _________ and our alpha value is 0.05. Therefore, we _____________ the null hypothesis and conclude that there _______________ a significant difference of exercise type on ___________________.

3. State your hypotheses for One-Way ANOVA analyzing the relationship between exercise type and depression:

4. Looking at the ANOVA table above. Write your conclusion below.

9. Based upon the results of the two, One-Way ANOVA’s, should you run any post hoc tests? Why or why not?

Simple Linear Regression

10. You believe that exercise can help decrease symptoms of stress and depression. On the PHLS 451 Survey, you measured the amount of time people spend exercising each week, as well as symptoms of stress and depression.

You decide to calculate two simple regression analyses. The first analysis looks at the linear relationship between time spent exercising and stress. The second analysis look sat the linear relationship between time spent exercising and depression. Results of both are below:

1. State your hypotheses for the relationship between time spent exercising and stress. Remember, your hypotheses should be written using β.

2. Looking at the output below, fill in the blanks in the conclusion paragraph below.

Looking at the Coefficients Table, the slope associated with time spent exercising each week is ________ and the p-value associated with time spent exercising is ________. The p-value of 0.036 is ________ the alpha value of 0.05. Therefore, we ______________ the null hypothesis and conclude that there _______ a linear relationship between time spent exercising and stress.

3. State your hypotheses for the relationship between time spent exercising and depression. Remember, your hypotheses should be written using β.

4. Looking at the output below. Write your conclusion regrading the linear relationship between time spent exercising and depression.

T-Tests

11. You believe that stress, depression, and well-being differ significantly between individuals who are employed and individuals who are unemployed. On the PHLS 451 Survey, you asked if people were currently employed or currently unemployed.

You decide to run three t-tests to compare the stress level, depression level, and self-reported well-being for individuals who are employed versus unemployed.

1. You will run the same type of t-test for all of three analyses. Which type of t-test will you run?

One-Sample Paired-Sample Independent-Sample

2. State your hypotheses for the relationship between unemployment and stress.

3. State your hypotheses for the relationship between unemployment and depression.

4. State your hypotheses for the relationship between unemployment and well-being.

e. Looking at the output below, fill in the missing information in the conclusion paragraph written below.

The purpose of this project was to explore differences in stress, depression, and self-report well-being with people who are employed versus unemployed. To analyze these results, we conducted three, ___________-Sample t-Test. The first t-test focused on the relationship between employment and unemployment on levels of stress. The mean stress level for employed individuals was __________, whereas the mean stress level for unemployed individuals was _______________. Looking at the results from the t-test, we see that the p-value associated with employment and stress was 0.006, which is less than our alpha value of 0.05. Therefore, we __________ the null hypothesis and conclude that stress levels differ significantly between employment levels.

The second t-test focused on the relationship between employment and unemployment on depression. The mean depression score for employed individuals was 3.00, whereas the mean stress level for unemployed individuals was 3.52. Looking at the results from the t-test, we see that the p-value associated with employment and depression was ____________, which is less than our alpha value of 0.05. Therefore, we __________ the null hypothesis and conclude that stress levels _________________ between employment levels.

Finally, the third t-test focused on the relationship between employment and unemployment on self-reported well-being. The mean self-reported well-being score for employed individuals was __________, whereas the mean well-being score for unemployed individuals was _______________. Looking at the results from the t-test, we see that the p-value associated with employment and stress was ______________, which is less than our alpha value of 0.05. Therefore, we __________ the null hypothesis and conclude that well between employment levels.

Extra Credit Problem

12. You believe screen time influences levels of stress and depression. Below are the results of two, simple linear regression analysis. Write a conclusion paragraph summarizing the results. Use an alpha value of 0.10 when making your decisions.
13. Your professor believes that time spent in nature is positively related to feelings of psychological well-being. Below are results of a simple linear regression. Write a conclusion paragraph summarizing the results. Use an alpha value of 0.10 when making your decision.

One-Way ANOVA

Answer 1

Answer:

Q.1 Which scale of measurement was used when measuring stress?

Nominal                            Ordinal               Ratio     Interval

Explanation: Looking at the options, it is clear that scale of measurement used here is ordinal scale since it follows particular order.

Q.2 Daily screen time was measured in minutes (e.g. 30 minutes, 60 minutes, 480 minute). Which scale of measurement was used to measure daily screen time?

Nominal             Ordinal Ratio     Interval

Explanation: Here the numbers in the variable are used only to classify the data so measurement scale here is Nominal scale.

Q.3 Employment was measured by selecting either “employed” or “unemployed”. Which scale of measurement was used to measure employment?

Nominal             Ordinal Ratio     Interval

Explanation: Same as Q.2, both options are given to classify the data, so measurement scale is here also Nominal scale.

Q.4 Is employment a categorical variable?

Yes        No         I don’t know

Q.5 One of the predictions for this project is that the amount of time an individual spends looking at screens the higher their stress level.

In this prediction, what is the independent variable and what is the dependent variable?

Independent Variable: Stress level

Dependent Variable: time spends on looking at screen

Q.6 One of the predictions for this project is that unemployment influences stress.

Which type of statistical analysis would you use to analyze this prediction?

t-test                   ANOVA               Correlation         Regression

For prediction analysis, Regression is used.

PTO

Q.7 Calculate the mean, median, and mode for each line of data below. Show your work.

Q1	Q2	Q3	Q4	Q5	Q6	Q7		Mean	Median	Mode
3	3	2	2	2	3	2		2.4	2	2
2	1	2	1	1	3	3		1.8	2	1
2	3	3	3	3	2	3		2.7	3	3
2	3	3	3	3	2	3		2.7	3	3

Explanation:

Formula to calculate mean= Sum of observations/total number of observations

So, for first line, Mean=3+3+2+2+2+3+2/6 =17/7 = 2.4

Median can be calculated by arranging all observations in either ascending or descending order, and median is middle most number of arranged data.

So, for first line, we will arrange data in ascending order :

2 2 2 2 3 3 3

Here middle most value is 2 hence, median is 2

Mode of the data means observation with highest frequency.

For first line, observation 2 is repeated four times on the other hand, 3 is repeated three times.

So, here Mode is 2.

Q.8 One-Way ANOVA

You are interested in how different types of exercise influence stress level and depression. On the PHLS 451 Survey, you asked which type of exercise people engage in the most. You also measured stress and depression using two different scales.

Since you are interested in two different dependent variables (i.e. stress and depression), you decide to run two, One-Way ANOVA’s.

Below are the results of both One-Way ANOVA’s.

Write your alternative and null hypotheses for the One-Way ANOVA analyzing the relationship between exercise time and stress:

Null hypothesis: There is no significant difference between means of exercise time and stress.

Alternative hypothesis: There is significant difference between means of exercise time and stress.

Looking at the ANOVA table above. Fill in the blanks below.

Looking at the results of the One-Way ANOVA, our p-value is ____0.591_____ and our alpha value is 0.05. Therefore, we _____do not reject________ the null hypothesis and conclude that there ________is not_______ a significant difference of exercise type on __stress_________________.

State your hypotheses for One-Way ANOVA analyzing the relationship between exercise type and depression:

Null hypothesis: There is no significant difference between means of exercise time and depression.

Alternative hypothesis: There is significant difference between means of exercise time and depression.

Looking at the ANOVA table above. Write your conclusion below.

Conclusion: Our p-value is 0.132 which is > alpha value i.e, 0.05. Therefore we do not reject null hypothesis and conclude that there is no significant relation between exercise and depression.

9. Based upon the results of the two, One-Way ANOVA’s, should you run any post hoc tests? Why or why not?

Answer: Since our both results are not significant, we can not go for post hoc test.

Simple Linear Regression

You believe that exercise can help decrease symptoms of stress and depression. On the PHLS 451 Survey, you measured the amount of time people spend exercising each week, as well as symptoms of stress and depression.

You decide to calculate two simple regression analyses. The first analysis looks at the linear relationship between time spent exercising and stress. The second analysis look sat the linear relationship between time spent exercising and depression. Results of both are below:

State your hypotheses for the relationship between time spent exercising and stress. Remember, your hypotheses should be written using ß.

Null hypothesis: Slope (ß)=0

Alternative hypothesis: Slope (ß) is not = to 0.

Looking at the output below, fill in the blanks in the conclusion paragraph below.

Looking at the Coefficients Table, the slope associated with time spent exercising each week is ___0.002_____ and the p-value associated with time spent exercising is ___0.036_____. The p-value of 0.036 is ____less than____ the alpha value of 0.05. Therefore, we _____reject_________ the null hypothesis and conclude that there __is_____ a linear relationship between time spent exercising and stress.

State your hypotheses for the relationship between time spent exercising and depression. Remember, your hypotheses should be written using ß.

Looking at the output below. Write your conclusion regarding the linear relationship between time spent exercising and depression.

Conclusion: Looking at the Coefficients Table, the slope associated with time spent exercising each week is ____0.001____ and the p-value associated with time spent exercising is ___0.001_____. The p-value of 0.119 is ____greater than____ the alpha value of 0.05. Therefore, we ____do not_reject_________ the null hypothesis and conclude that there __is no_____ a linear relationship between time spent exercising and stress.

T-Tests

You believe that stress, depression, and well-being differ significantly between individuals who are employed and individuals who are unemployed. On the PHLS 451 Survey, you asked if people were currently employed or currently unemployed.

You decide to run three t-tests to compare the stress level, depression level, and self-reported well-being for individuals who are employed versus unemployed.

You will run the same type of t-test for all of three analyses. Which type of t-test will you run?

One-Sample Paired-Sample Independent-Sample

Answer: Independent Sample T-test

State your hypotheses for the relationship between unemployment and stress.

H0: There is no relationship between unemployment and stress

H1: There is relationship between unemployment and stress

State your hypotheses for the relationship between unemployment and depression.

H0: There is no relationship between unemployment and depression

H1: There is relationship between unemployment and depression

State your hypotheses for the relationship between unemployment and well-being.

H0: There is no relationship between unemployment and well being

H1: There is relationship between unemployment and well being

e. Looking at the output below, fill in the missing information in the conclusion paragraph written below.

The purpose of this project was to explore differences in stress, depression, and self-report well-being with people who are employed versus unemployed. To analyze these results, we conducted three, ___Independent ________-Sample t-Test. The first t-test focused on the relationship between employment and unemployment on levels of stress. The mean stress level for employed individuals was ____2.54______, whereas the mean stress level for unemployed individuals was ___3.16____________. Looking at the results from the t-test, we see that the p-value associated with employment and stress was 0.006, which is less than our alpha value of 0.05. Therefore, we ___reject_______ the null hypothesis and conclude that stress levels differ significantly between employment levels.

The second t-test focused on the relationship between employment and unemployment on depression. The mean depression score for employed individuals was 3.00, whereas the mean stress level for unemployed individuals was 3.52. Looking at the results from the t-test, we see that the p-value associated with employment and depression was _____0.018_______, which is less than our alpha value of 0.05. Therefore, we ____reject______ the null hypothesis and conclude that depression levels __________differ significantly_______ between employment levels.

Finally, the third t-test focused on the relationship between employment and unemployment on self-reported well-being. The mean self-reported well-being score for employed individuals was _____4.844_____, whereas the mean well-being score for unemployed individuals was _______5.271________. Looking at the results from the t-test, we see that the p-value associated with employment and stress was ______0.271________, which is greater than our alpha value of 0.05. Therefore, we ____do not reject______ the null hypothesis and conclude that well between employment levels.

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