**Learning and Applying Tests of Significance**

__Mock Study 1: t-Test for a Single Sample (15 points)__

__Mock Study 1: t-Test for a Single Sample (15 points)__

*Research hypothesis (H*_{1}) and null hypothesis (H_{0}).

**H**The average number of Activities of Daily Living (ADL) obtained after therapy is significantly different from the mean number of activities (15) that is typical for depressed people_{1}:**H**The average number of Activities of Daily Living (ADL) obtained after therapy is not significantly different from the mean number of activities (15) that is typical for depressed people_{0}:*H*_{1}: x̄ = 15 vs H_{0}: x̄ ≠ 15

- The significance level (alpha) used in the current mock study is at .05 and .01. The results of BOTH .05 and .01 are to test the hypotheses.
- Analysis in SPSS.

One-Sample Test |
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Test Value = 15 | ||||||

t | Df | Sig. (2-tailed) | Mean Difference | 95% Confidence Interval of the Difference | ||

Lower | Upper | |||||

ADL | 1.619 | 19 | .122 | 1.650 | -.48 | 3.78 |

One-Sample Test |
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Test Value = 15 | ||||||

t | Df | Sig. (2-tailed) | Mean Difference | 99% Confidence Interval of the Difference | ||

Lower | Upper | |||||

ADL | 1.619 | 19 | .122 | 1.650 | -1.27 | 4.57 |

- The p-value obtained for both 0.05 and 0.01 significance levels is 0.122
- The p-value obtained indicates that the p-value (0.122) is larger than the alpha 0.05 and 0.01. According to the decision rule, this indicates that we should accept the null hypothesis and conclude that the average number of Activities of Daily Living (ADL) obtained after therapy is not significantly different from the mean number of activities (15) that is typical for depressed people. Since there is no significant difference, the scientists should find alternative methods of therapy for depressed people that will increase the number of ADLs for positive outcomes other than group therapy programs.

__Mock Study 2: t- Test for Dependent Means (15 points)__

__Mock Study 2: t- Test for Dependent Means (15 points)__

- Research hypothesis (H
_{1}) and the null hypothesis (H_{0}).

**H**The observed differences in the number of activities of daily living obtained before and after therapy are statistically significant._{1}:**H**The observed differences in the number of activities of daily living obtained before and after therapy are not statistically significant._{0}:

- The significance level (alpha) used in the current mock study is at .05.
- The SPSS Analysis output

Paired Samples Test |
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Paired Differences | t | df | Sig. (2-tailed) | ||||||

Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | ||||||

Lower | Upper | ||||||||

Pair 1 | ADLPRE – ADLPOST | -4.300 | 3.199 | 1.012 | -6.588 | -2.012 | -4.251 | 9 | .002 |

- The p-value obtained is 0.002 at a .05 level of significance.
- The p-value (0.002) is smaller than the alpha value of 0.05. Based on the decision rule, we reject the null hypothesis and conclude that the observed differences in the numbers of activities of daily living obtained before and after therapy are statistically significant. This provides sufficient evidence that indicates that scientists should recommend group therapy for all depressed people.

__Mock Study 3: t-Test for Independent Samples (15 points)__

__Mock Study 3: t-Test for Independent Samples (15 points)__

- Research hypothesis (H
_{1}) and the null hypothesis (H_{0}).

**H**The job satisfaction scores of the group that participated in a counseling session are statistically different from the scores of employees who chose not to participate in counseling sessions._{1}:**H**The job satisfaction scores of the group that participated in a counseling session are not statistically different from the scores of employees who chose not to participate in counseling sessions._{0}:

- The test of the hypothesis is performed at a 0.01 level of significance.
- SPSS Analysis

Independent Samples Test |
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Levene’s Test for Equality of Variances | t-test for Equality of Means | |||||||||

F | Sig. | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference | |||

Lower | Upper | |||||||||

ADL | Equal variances assumed | 1.337 | .263 | 1.706 | 18 | .105 | 2.200 | 1.289 | -.509 | 4.909 |

Equal variances not assumed | 1.706 | 15.676 | .108 | 2.200 | 1.289 | -.538 | 4.938 |

- The p-value obtained under the t-test for equality of means is 0.105.
- The p-value obtained is larger than the alpha value (0.01) set for the study. According to the decision rule, we should accept the null hypothesis and conclude that the job satisfaction scores of the group that participated in counseling session are not statistically different from the scores of employees who chose not to participate in counseling sessions. These findings provide a basis to conclude that counseling is not an effective method to improve job satisfaction following industrial accidents.

__Mock study 4: One-Way ANOVA__

__Mock study 4: One-Way ANOVA__

- Research hypothesis (H
_{1}) and null hypothesis (H_{0}).

**H**The observed differences in the number of hours watching TV across three groups are statistically significant_{1}:**H**The observed differences in the number of hours watching TV across three groups are not statistically significant._{0}:

- The level of significance for the mock study is alpha at .05
- SPSS Analysis

ANOVA |
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Hours per day watching TV | |||||

Sum of Squares | df | Mean Square | F | Sig. | |

Between Groups | 409.066 | 2 | 204.533 | 26.236 | .000 |

Within Groups | 12099.008 | 1552 | 7.796 | ||

Total | 12508.073 | 1554 |

- The p-value obtained is a small number, reported as p<.0001.
- This indicates that the p-value is less than alpha value of 0.05. Based on the decision rule, we should reject the null hypothesis and conclude that the observed differences in the number of hours watching TV across three groups are statistically significant. This provides an evidence that the advertising firm should target each racial group differently since their TV watching habits differ significantly.

**Circumstances when ANOVA is appropriate compared to t-test: **Although t-test and ANOVA all test differences between groups, the ANOVA test is appropriate when testing differences for more than one group. This is why t-tests are referred as special types of ANOVA.

__Mock Study 5: Chi-Square Test for Independence__

__Mock Study 5: Chi-Square Test for Independence__

- Research hypothesis (H
_{1}) and null hypothesis (H_{0}).

**H**The observed frequency is significantly different from the expected frequency._{1}:**H**The observed frequency is not significantly different from the expected frequency_{0}:

- The level of significance for the test of independence is .05.
- SPSS Analysis

Chi-Square Tests |
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Value | df | Asymptotic Significance (2-sided) | |

Pearson Chi-Square | 27.658^{a} |
14 | .016 |

Likelihood Ratio | 27.897 | 14 | .015 |

Linear-by-Linear Association | 4.754 | 1 | .029 |

N of Valid Cases | 1506 | ||

a. 1 cells (4.2%) have an expected count of less than 5. The minimum expected count is 2.73. |

- The analysis indicates that the Pearson Chi-Square p-value is 0.016.
- The p-value is smaller than 0.05. Based on the decision rule, we should accept the null hypothesis and conclude that the observed frequency is significantly different from the expected frequency. This provides evidence to conclude that an individual’s political party affiliation affects their confidence in Congress.

__Mock study 6: Linear Regression__

__Mock study 6: Linear Regression__

- Research hypothesis (H
_{1}) and null hypothesis (H_{0}).

**H**Age affects the number of poor mental health days_{1}:**H**Age does not affect the number of poor mental health days_{0}:

- The level of significance used for the model is .05.
- SPSS Analysis

ANOVA^{a} |
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Model | Sum of Squares | df | Mean Square | F | Sig. | |

1 | Regression | 611.395 | 1 | 611.395 | 12.917 | .000^{b} |

Residual | 66266.114 | 1400 | 47.333 | |||

Total | 66877.509 | 1401 | ||||

a. Dependent Variable: Days of poor mental health past 30 days | ||||||

b. Predictors: (Constant), Age of respondent |

- The p-value obtained is .000, reported as p<.0001.
- The p-value obtained is smaller than the level of significance. This indicates that we should reject the null hypothesis and conclude that age affects the number of poor mental health days. This shows a relationship between age and poor mental health days

**The Model **

Coefficients^{a} |
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Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||

B | Std. Error | Beta | ||||

1 | (Constant) | 5.602 | .594 | 9.425 | .000 | |

Age of respondent | -.047 | .013 | -.096 | -3.594 | .000 | |

a. Dependent Variable: Days of poor mental health past 30 days |

*Y= 5.602 – 0.047X _{1}*

*Where Y= Poor Mental Health Days*

*X _{1}= Age of the respondent*.

Therefore, the model indicates that age is negatively related to poor mental health days.

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**Question**

Complete the following assignment by filling in all requested information. In this assignment, you will review mock studies and analyze data within each study. You will need to CAREFULLY follow the directions outlined in each section of the attached document using SPSS. Some of the studies require you to enter data, and some require you to use the GSS data set. You will list the five steps of hypothesis testing for each Mock Study to see how every question should be formatted. You will decide whether to reject or fail to reject the null hypothesis. Be sure to cut and paste the appropriate SPSS outputs under each problem and interpret the outputs within the context of each mock study. Use a different (legible) color font for your responses.

Throughout this assignment, you will review six mock studies. Follow the step-by-step instructions:

- Mock Studies 1 – 3 require you to enter data from scratch. You need to create a data set for each of the three mock studies by yourself. (Refresh the data entry skill acquired in Week 1.)
- Mock Studies 4 – 6 require you to use the GSS 2018 dataset. The variables are specified in each Mock Study.
- Go through the five steps of hypothesis testing (below) for EVERY mock study.
You will need to submit the SPSS output file (.spv) to get credit for this assignment.**All calculations should be coming from your SPSS.**

__The five steps of hypothesis testing when using SPSS are as follows:__

- State your research hypothesis (H
_{1}) and null hypothesis (H_{0}). - Identify your significance level (alpha) at .05 or .01, based on the mock study. In Mock Study One, you are required to use BOTH .05 and .01 to test your hypotheses. For the remaining mock studies, you only need to use ONE level of significance (either .05 or .01) as specified in the instructions.
- Conduct your analysis using SPSS.
- Look for the valid score for comparison. This score is usually under ‘Sig 2-tail’ or ‘Sig. 2’ or ‘Asymptotic Sig.’ We will call this “p.”
- Compare the two and apply the following rule:
- If “p” is < or = alpha, then you reject the null.
- Please explain what this decision means in regard to this mock study. (Ex: Will you recommend counseling services?)

Please make sure your answers are clearly distinguishable. Perhaps you could bold your font or use a different color.