This is a course level assessment assignment. MM570-2: Compare group means with a single or multiple independent variables using the appropriate statistical test.
Rubric for Unit 6 Assignment
MM570 Unit 6 Assignment Grading Rubric | |
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 t-test 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. (2-tailed) 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, including the statement of the hypothesis, inclusion of the null and alternative hypothesis Ho and Ha, results from the hypothesis t-test, and complete clearly written conclusions. |
For this Project, you will use the “Statistics Class” dataset called Stat_Grades.sav, which can be found in the Doc Sharing area under the Graded Projects category. This same “Statistics Class” dataset is used for all the class projects. The Stat_Grades.sav dataset contains data collected about students in three sections of a statistics class taught by an instructor. You will also use SPSS for this project.
HINTS AND HELP
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 hypothesis testing question, follow the appropriate steps.
1) Write the hypothesis
2) Construct the Ho and Ha clearly and appropriately. Note the means you are comparing.
3) Run the appropriate SPSS test 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.
Place all answers, work, and graphs in this document.
Use alpha = .05 for all hypothesis testing questions.
** Please use non-directional two-tailed tests for these questions (not one-tailed tests).
- Recall that the dataset, Stat_grades.sav, contains data for a sample of 105 statistics students. One of the variables in this dataset is called, gender. This variable is either “1” for “Female”, or “2” for “Male”. The Instructor is wondering if gender affects student performance as measured using Final Course Percentage (called Percent) . Using the appropriate statistical test, methods, and evaluations, determine if Gender made a significant difference in Final Course Percent. Be sure to include each step of the process, any SPSS results used, an interpretation of the results, and the final conclusions.
(a) What is the hypothesis being tested here?
Hypothesis
The hypothesis is to determine if there is a statistically significant difference in the average Total Points between the different class sections.
(b) What are Ho and Ha?
Ho: the average total point between the different class section are equal
Vs
Ha: there exist at least one section whose mean differs from others.
(c) What is the name of the test you will run? Run the appropriate SPSS test and include the SPSS output here.
The statistical test used is one-way ANOVA.
(d) What are the results of the test? What is the p-value and is it larger or smaller than the alpha value – show your work and explain the result.
Table 1.
Descriptives | ||||||||
total | ||||||||
N | Mean | Std. Deviation | Std. Error | 95% Confidence Interval for Mean | Minimum | Maximum | ||
Lower Bound | Upper Bound | |||||||
1 | 33 | 105.09 | 16.148 | 2.811 | 99.36 | 110.82 | 51 | 124 |
2 | 39 | 99.49 | 12.013 | 1.924 | 95.59 | 103.38 | 75 | 124 |
3 | 33 | 97.33 | 17.184 | 2.991 | 91.24 | 103.43 | 52 | 122 |
Total | 105 | 100.57 | 15.299 | 1.493 | 97.61 | 103.53 | 51 | 124 |
Table 2.
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 |
Table 3.
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. |
Table 4.
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 |
Graph 1.
From the result so far we can get to know that there is a statistical difference from between the sections as a whole. Therefore this confirms the results, but from the table 4 above multiple comparisons show the sections that differ from each other. From the table, we can see there is the statistical difference between section 1 and 1(p-value=0.264) as well as the sections 3 and 1(p-value=0.98). However, there is no difference between the section 3 and 2(p-value=0.819). Therefore post hoc is needed in this case. From the graph we can see that section 1 has the highest mean followed by section 2 and section 3 has the lowest mean.
(e) Write a conclusion for the above in plain English so that any person could understand. What can you say about gender and its effect on overall performance?
In conclusion, we can say that section 1 had the highest mean of 105.09 with the standard deviation of 16.148 followed by section 2 with the mean of 99.49 and standard deviation of 12.013 and finally section 3 with the mean of 97.33 and standard deviation of 17.184. At an average, these class sections had a mean of 100.57 with the standard deviation of 15.299. The test shows as shown in table 2 the significance value is 0.102(p=0.102) which is above 0.05. Therefore, there is no statistically significant difference in the means score of the class sections. This means we accept the null hypothesis H0
- Based on many years of past classes and experience, the Instructor for the students in the Stat_Grades.sav dataset has determined that a successful mean value for Total Points is 90 points. Does the Total Points for the students in Stat_Grades.sav differ significantly from the known success value of 90 points? Use and include the appropriate statistical test, methods, and evaluations. Be sure to include each step of the process, any SPSS results used, an interpretation of the results, and final conclusions.
(a) What is the hypothesis being tested here?
The statistically significant difference in the average Total Points between the different sections and different genders.
(b) What are Ho and Ha?
H0: the average total points between the different sections and different gender are equal.
vs
Ha: there exist at least one total points between the different sections and different gender that differs from others.
(c) What is the name of the test you will run? Run the appropriate SPSS test and include the SPSS output here.
Table 5.
Descriptives | ||||||||
gender | ||||||||
N | Mean | Std. Deviation | Std. Error | 95% Confidence Interval for Mean | Minimum | Maximum | ||
Lower Bound | Upper Bound | |||||||
1 | 33 | 1.39 | .496 | .086 | 1.22 | 1.57 | 1 | 2 |
2 | 39 | 1.33 | .478 | .076 | 1.18 | 1.49 | 1 | 2 |
3 | 33 | 1.45 | .506 | .088 | 1.28 | 1.63 | 1 | 2 |
Total | 105 | 1.39 | .490 | .048 | 1.30 | 1.49 | 1 | 2 |
Table 6.
ANOVA | |||||
gender | |||||
Sum of Squares | Df | Mean Square | F | Sig. | |
Between Groups | .263 | 2 | .132 | .543 | .583 |
Within Groups | 24.727 | 102 | .242 | ||
Total | 24.990 | 104 |
Table 7.
Multiple Comparisons | ||||||
Dependent Variable: gender | ||||||
Tukey HSD | ||||||
(I) section | (J) section | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval | |
Lower Bound | Upper Bound | |||||
1 | 2 | .061 | .116 | .862 | -.22 | .34 |
3 | -.061 | .121 | .871 | -.35 | .23 | |
2 | 1 | -.061 | .116 | .862 | -.34 | .22 |
3 | -.121 | .116 | .553 | -.40 | .16 | |
3 | 1 | .061 | .121 | .871 | -.23 | .35 |
2 | .121 | .116 | .553 | -.16 | .40 |
Table 8
Gender | ||
Tukey HSD^{a,b} | ||
Section | N | Subset for alpha = 0.05 |
1 | ||
2 | 39 | 1.33 |
1 | 33 | 1.39 |
3 | 33 | 1.45 |
Sig. | .562 | |
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. |
Graph 2.
(d) What are the results of the test? What is the p-value? Compare the p value to alpha and note the result.
From the result so far we can get to know that there is no statistical difference from between the sections as a whole. Therefore this confirms the results, and this is confirmed in table 7 above that shows multiple comparisons. From this table we can see there is no statistical significance between section 1 and2,1 and 3 and 2 and 3.this is because their p-values are 0.862,0.871 and 0.553 respectively which are higher than 0.05.
(e) Explain the conclusion in plain English so that any person could understand. Did the students in Stat_Grades.sav do significantly differently than the population mean of 90? How did they do and what did you find? Explain.
In conclusion, we can say that section 3 had the highest mean of 1.45 with a standard deviation of 0.506 followed by section 1 with the mean of 1.39 and standard deviation of 0.496 and finally section 1 with the mean of 1.33 and standard deviation of 0.478. At an average, these class sections had a mean of 1.39 with a standard deviation of 0.49. The test shows as shown in table 6 the significance value is 0.583(p=0.583) which is above 0.05. Therefore there is no statistically significant difference in the means score of the class sections. This means we accept the null hypothesis H0.
- Using the Stat_Grades.sav dataset, compare Quiz 1 and Quiz 2 to determine if there is a statistically significant difference in the average student performance between these two quizzes. Use and include the appropriate statistical test, methods, and evaluations. Be sure to include each step of the process, any SPSS results used, an interpretation of the results, and final conclusions.
(a) What is the hypothesis being tested here?
The statistically significant difference in the average Total Points between the students performance and different quizzes.
(b) What are Ho and Ha?
H0: the average total points between the different sections and different quizzes are equal.
vs
Ha: there exist at least one total points between the different students and different quisses that differs from others.
(c) What is the name of the test you will run? Run the appropriate SPSS test and include the SPSS output here.
The statistical test used is one-way ANOVA.
(d) What are the results of the test? What is the p-value? Compare the p value to alpha and note the result.
(e) Explain the result and conclusion of the test in plain English so that any person could understand.
In conclusion, we can say that average Total Points between the students performance and different quizzes. Out of the five quizzes, the numeric value is between 1 an 3 . At an average, there are those who have scale and nominal performance. Therefore, there is no statistically significant difference in the means score based on the different quizzes. This means we accept the null hypothesis H0
- Use the following SPSS output to answer these questions. The hypothesis here is: “Is there a significant difference in Final Exam Points between lower division students and upper division students (variable: lowup)?”
(a) What is Ho and Ha?
H0: the difference between in final exam points between the upper and lower division students are equal.
vs
Ha: there exist at different in final points between the lower division students and upper division students that differs from others
(b) What t-test is being used?
The Chi T Test.
(c) What is the p value? (Assume equal variances)
(d) Using alpha at .05, what is the result of this test?
Y=59.999+5.202X
Y= 59.999+5.202(8)
Y=100.159
Therefore total points for quiz4 (8) is 100.159.
(e) Write the full conclusion for this test in plain English so anyone can understand.
(f) How many Lower Division students are in this sample of data? Is the mean points for lower division students different than it is for upper division students? Is it significantly different? What does it mean to be significantly different (versus just different)?
From the above spss output, R-value is .775. This indicates a high degree of correlation between the two variable. Therefore it is strong enough to allow prediction between these two variables. This is because R-value(r=.775)>0.5.
R=0.445
Which is medium.
This means R-value is not strong enough to use for prediction.