**Unit 9 Project: Descriptive Statistics**

**This is a course level assessment assignment. MM570-3:** Interpret correctly the output from SPSS analyses/statistical tests.

**Your Name: **

**HINTS AND HELP**

**Dataset:**** Stat_Grades.sav can be found in Doc Sharing under the Instructor Graded Projects category. **

**Note:**** When asked to include the interpretation of the results and final conclusions, be sure to include all results, an interpretation of the meaning of the results, and final conclusions that a common person can understand. Make sure you use complete sentences, paragraph form (single spacing), proper grammar, and correct spelling. Minimal or incomplete responses can lose points. Include any SPSS results that you use, but do not include SPSS results that are not part of your solution**

**Hint:**** You are asked to determine “appropriate” tests and methods, and to make calculations. This means that you will have to determine which tests or methods are best and why. **

**Remember** **to always show all of your work and each of your steps.**

For each question, follow the appropriate steps.

1) Write the hypothesis – Construct the null(s) and alternative(s) clearly and appropriately.

3) Run the appropriate SPSS test(s) and include the appropriate results

4) Explain and evaluate the SPSS results

5) Write a complete and paragraph form conclusion that can be understood by a normal non-statistical person.

**Use the Live Binder for further assistance. There is a link to the Live Binder under every Unit.**

Point Possible |
Grading Criteria |

A: 153 – 170 points | Student work demonstrates mastery of the objectives assessed by the Assignment. This is evidenced by at least the following:
· The selection of the statistical procedure(s) is/are the most appropriate ones for answering the questions; specifically, the correct ANOVA test method is selected for each question. · The statistical procedure was calculated correctly using SPSS. · The interpretation of the SPSS output is correct and complete, including applying the (Sig. in SPSS) p-value to determine null hypothesis rejection. · The results of the statistical analyses are presented in easy to understand, non-statistical language that addresses the research question. · SPSS output that is not needed in the solution is not included. Only appropriate SPSS output are included. · Each step of the hypothesis testing procedure is included and Ho and Ha are clearly written. · All aspects of the tests are included and explained, including the Post Hoc results and the interaction plot. · Appropriate regression prediction equations are created and evaluated. |

**Use alpha = .05 for this project. **

- Compare the different
**Sections (1, 2, and 3)**of students in the Stat_Grades.sav dataset to determine if there is a statistically significant difference in the average**Total Points**between the different class sections. In other words, just like at Kaplan, there are different sections of the same class. The dataset Stat_Grades.sav has data from three sections of statistics classes. Be sure to state the hypothesis, state Ho and Ha, include and explain all SPSS results, and write final conclusions for the full results of the test.__Include Post Hoc__results and the__plot__. Be sure that your final conclusions are written in common terms for an average person to understand.

**(a) What is the hypothesis being tested?**

The hypothesis being tested is whether there is a statistically significant different in the average total points between the different class sections.

**(b) What are Ho and Ha?**

**H _{0}:** There is no any statistically significant difference in the average Total Points between the different class sections.

**Ha:** There is a statistically significant difference in the average Total Points between the different class sections.

**(c) What statistical test will you run – and include all the SPSS outputs (including the plot and post hoc)?**

I will run one-way anova because the variables are more than two. Here are the results of the analysis.

ANOVA |
|||||

total | |||||

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

Between Groups | 1065.910 | 2 | 532.955 | 2.335 | .102 |

Within Groups | 23277.804 | 102 | 228.214 | ||

Total | 24343.714 | 104 |

POST HOC Test

Multiple Comparisons |
||||||

Dependent Variable: total | ||||||

Tukey HSD | ||||||

(I) section | (J) section | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval | |

Lower Bound | Upper Bound | |||||

1 | 2 | 5.604 | 3.573 | .264 | -2.89 | 14.10 |

3 | 7.758 | 3.719 | .098 | -1.09 | 16.60 | |

2 | 1 | -5.604 | 3.573 | .264 | -14.10 | 2.89 |

3 | 2.154 | 3.573 | .819 | -6.34 | 10.65 | |

3 | 1 | -7.758 | 3.719 | .098 | -16.60 | 1.09 |

2 | -2.154 | 3.573 | .819 | -10.65 | 6.34 |

total |
||

Tukey HSD^{a,b} |
||

section | N | Subset for alpha = 0.05 |

1 | ||

3 | 33 | 97.33 |

2 | 39 | 99.49 |

1 | 33 | 105.09 |

Sig. | .087 | |

Means for groups in homogeneous subsets are displayed. | ||

a. Uses Harmonic Mean Sample Size = 34.784. | ||

b. The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed. |

Mean Plots

**(d) Explain the full results for the statistical test that you ran above. Was a post hoc actually needed in this case? Why or why not? Does the Post Hoc confirm your results, explain? What does the plot tell you about the interaction, explain?**

The p-value from Anova table is 0.106. The value is greater than 0.05 level of significance. Since the p-value from Anova table is greater than 0.05 level of significance, we fail to reject the null hypothesis. The Anova table does not say much about the effect size, therefore, it was necessary to do a post hoc analysis. The post hoc test shows that there is no statistically significant difference in the average Total Points between the different class sections. The plot indicates that there is an interaction effect.

**(e) Write a full conclusion for all results on this test in a way that can be understood by a non-statistical person. This answer will be at least 100 words or more. **

This test was conducted to determine whether there a was statistically significant difference in the average total points between different class sections. Since the variables are more than 3, Anova test was found to be suitable test to do the analysis. From the results of the one-way Anova test, we failed to reject the null hypothesis because the p-value from the test was greater than 0.05 level of significance. Further tests such as the post hoc test was conducted to confirm this revelation. The post hoc test also indicated that there was no statistically significant difference in the average total between different class sections. Therefore, from the analysis we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim at 5% level of significance. There is no statistically significant difference in the average total points between the different class sections.

**Extend the hypothesis from number one above. Compare the different sections in the Stat_Grades.sav dataset**__and__the genders to determine if there is a*statistically significant difference in*the average Total Points between the different sections__and__different genders. Be sure to state the hypothesis, state all Ho and Ha, include and explain all SPSS results, and write final conclusions for the full results of the test. Include Post Hoc results, note any interactions and whether they are significant, and include and explain the plot. Be sure that your final conclusions are written in common terms for an average person to understand.

**What is the hypothesis being tested?**

If there is a statistically significant difference in the average Total Points between the different class sections with regards to gender.

**What are the set of Ho’s and Ha’s?**

**H _{0}:** There is no any statistically significant difference in the average Total Points between the different genders.

**Ha:** There is a statistically significant difference in the average Total Points between the different genders.

**What statistical test will you run – and include all the SPSS outputs (including the plot and post hoc)?**

I will run one-way Anova test to test the differences in the means because the variables are more than two.

ANOVA |
|||||

total | |||||

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

Between Groups | 349.289 | 1 | 349.289 | 1.499 | .224 |

Within Groups | 23994.425 | 103 | 232.956 | ||

Total | 24343.714 | 104 |

**Explain the full results of the statistical test you have run. Was a post hoc actually needed in this case? Why or why not? Does the Post Hoc confirm your test results, explain? What does the plot tell you about the interaction, explain?**

The p-value from the Anova table is 0.224. The value is greater than 0.05 level of significance, therefore, we will fail to reject the null hypothesis. There are only two groups males and females, therefore, a post hoc test will not work. The plot shows that there is no interaction effect.

**Write a full conclusion for all results on this test in a way that can be understood by a non-statistical person. This answer will be at least 100 words or more.**

This analysis was conducted to determine if there is a significant difference in the average totals points in the different sections between males and females. A one-way anova test was conducted to test the differences between the means. From the anova table, the p-value was greater than the 5% significant level, therefore, we fail to reject the null hypothesis and conclude that there was no statistically significant difference in the average total points between males and females. It was not necessary to conduct a post hoc test because there were only two groups, that is males and females. Post hoc test requires more than two groups.

**Prediction and Regression. If you recall from the Unit 3 Project, you looked at how to measure the relationship (correlation) between any two variables. You also learned that if two variables are strongly correlated (related) with each other, that one variable can be used to estimate or predict the other. The equation used to make this prediction is called a regression equation.**

Use the following SPSS outputs to answer the questions. The two variables in this case are **Quiz 4 **and **Total Points**.

**(a) What are the two variables that this question is investigating? Notice that the SPSS output above tells you that the r-value (called “R”) is .775. Is this r-value strong enough to allow you to perform prediction between these two variables? Explain.**

The two variables that this question is investigating are Quiz 4 Points and Total Points. The Pearson’s correlation coefficient is 0.775. The positive and high correlation coefficient shows that there is a strong positive relationship between Quiz 4 Points and Total Points. Since, the correlation between the two variables is strong one can perform a prediction between the two variables.

(**b) Using the “Coefficients” SPSS output above, create the prediction equation. Remember that your independent or “x” variable is Quiz 4 and your dependent or “y” variable is Total Points. Write the prediction equation here.**

Prediction equation

Total Points = 59.999 + 5. 202 Quiz 4 Points

**(c) Using the prediction equation that you created in part (b), predict the Total Points for a student with a Quiz 4 ****score of 8. Show all work. **

Quiz 4 score of 8

Total Points = 59.999 + 5. 202 Quiz 4 Points

Total Points = 59.999 + 5. 202 (8)

Total Points = 59.999 + 41.616

Total Points = 101.615

** **

**From the Stat_Grades.sav dataset, use Quiz 4 and Quiz 5 to answer these questions. The question you will be considering here as you answer the questions below is***“Is the score on Quiz 4 highly correlated to the score on Quiz 5 and can one be used to estimate or predict the other?”*

**What is the correlation or relationship (r-value) between Quiz 4 and Quiz 5? Is it weak, medium, or strong? Is it strong enough to use for prediction?**

Correlations |
|||

quiz4 | quiz5 | ||

quiz4 | Pearson Correlation | 1 | .445^{**} |

Sig. (1-tailed) | .000 | ||

N | 105 | 105 | |

quiz5 | Pearson Correlation | .445^{**} |
1 |

Sig. (1-tailed) | .000 | ||

N | 105 | 105 | |

**. Correlation is significant at the 0.01 level (1-tailed). |

The correlation coefficient is 0.445. The value shows that there is a weak positive correlation between quiz 4 and quiz 5. The strength of this R-value is not enough to use for prediction.

**(b) Use SPSS and run a regression analysis on Quiz 4 and Quiz 5. Place the SPSS “Coefficients” output (only) here.**

Coefficients^{a} |
||||||

Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||

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

1 | (Constant) | 5.181 | .555 | 9.335 | .000 | |

quiz4 | .344 | .068 | .445 | 5.039 | .000 | |

a. Dependent Variable: quiz5 |

**Use the SPSS output to create the regression (prediction) equation. Remember, you are trying to***predict how a student will perform on Quiz 5 based on how they do on Quiz 4.*What is your dependent (y) variable? What is your independent (x) variable? Write the prediction equation here.

The dependent variable is quiz 5 while the independent variable is quiz 4.

Regression Equation

Quiz 5 = 5.181 + 0.344 quiz4

**Use your prediction equation to predict how a student would perform on Quiz 5 if they got a 6 on Quiz 4. Show all work.**

From the regression equation:

Quiz 5 = 5.181 + 0.344 quiz4

Quiz 5 = 5.181 + 0.344(6)

Quiz 5 = 5.181 + 2.064

Quiz 5 = 7.245

**Submitting your Project **

*Make sure your name is on your project and saved to your computer. When you are ready to submit your completed project, click on the Dropbox and complete the steps below: *

- Click the link that says “Submit an Assignment.”
- In the “Submit to Basket” menu, select Unit 9: Project.
- In the “Comments” field, include your name and Unit 9 Project.
- Click the “Add Attachments” button.
- Follow the steps listed to attach your Word document.
- You should revisit the Dropbox to view any helpful feedback your instructor has left for you.
- Make sure that you save a copy of your submitted and returned assignment.