Parametric and Non Parametric Analyses
Part 1
A principal wants to determine if a new ACT preparation program is effective. The data are contained in the schools.sav data file. Open the schools.sav file in SPSS. Use SPSS to determine whether a significant improvement existed between student performance on ACT tests in 1993 (act93) and ACT tests in 1994 (act94). Assume that the same students were involved in 1993 and 1994 testing. (This requires a t-test. Review Chapter 10 of the Green & Salkind text for information on paired t-tests and reporting APA results interpretation and writing.)
Create a report that answers the principal’s question. Write these conclusions in formal APA results format. Include your SPSS output to support your conclusion.
Part 2
A pharmaceutical company wants to determine whether there is a need for a new medication based on the data in the electric.sav file. Specifically, they want to determine whether a person is alive or dead 10 years after a coronary incident and whether that is reflected in a significant difference in the patients’ cholesterol levels (chol58) taken when the event occurred. Use chol58 as a dependent variable and VITAL10 as your independent variable. Complete the following:
- Analyze these conditions to determine whether there is a significant difference between the cholesterol levels (vital10) of those who are alive 10 years later compared to those who died within 10 years.
- Include the SPSS output, which validates your conclusion.
- Write a brief paragraph describing your conclusions.
Refer to Unit 6 in the Green & Salkind text for specific information about SPSS tests and APA results interpretation and writing. Pay attention to the Levene’s test throughout for determining whether the assumption of equal variance was met when you make your final decisions about the analysis.
What conclusion did you reach? Write these conclusions in formal APA results format. Include your SPSS output to support that conclusion.
Part 3
Occasionally, you have 1 independent variable that has 3 or more levels or groups. For a parametric data set, an analysis of variance (ANOVA) is the proper calculation. Use an ANOVA to address the following scenario:
A financial planner is interested in understanding the relationship between the dependent variable of the income level of respondents (rincdol) and the independent variable of their education level (ndegree) from the gss.sav data file. Use SPSS to complete the following:
- Run an ANOVA to determine the overall conclusion.
- Use the Bonferroni correction as a post-hoc analysis to determine the relationship of specific levels of degree level to income.
- Explain the overall conclusions based on the analysis, and describe the relationship(s) between the levels of the degree earned and income.
- Write your conclusion of the findings based upon the output using proper APA formatting.
Submit both the SPSS output file and your Word summary. (Refer to the Green & Salkind section about a one-way ANOVA for information on APA results interpretation and writing.)
Uni
t
3 IP Diagrams
Part 1
|
Paired Samples Statistics |
|||||||||||
|
Mean |
N |
Std. Deviation |
Std. Error Mean |
||||||||
|
Pair 1 |
average ACT score 1993 |
15.986 |
64 |
1.8401 |
. 2 300 |
||||||
|
average ACT score 1994 |
15.8 61 |
1.8351 |
.2294 |
|
Paired Samples Correlation s |
|||||||
| Correlation |
Sig. |
||||||
|
average ACT score 1993 & average ACT score 1994 |
.972 |
.000 |
|
Paired Samples Test |
||||||||||
|
Paired Differences |
t |
df |
Sig. (2-tailed) |
|||||||
|
95% Confidence Interval of the Difference |
||||||||||
|
Lower |
Upper |
|||||||||
|
average ACT score 1993 – average ACT score 1994 |
.1250 |
.4342 |
.0543 |
.0165 |
.2335 |
2.303 |
63 |
.025 |
|
Paired Samples Effect Sizes |
||||||
|
Standardizera |
Point Estimate |
95% Confidence Interval | ||||
|
Cohen’s d |
.288 |
.037 |
.537 |
|||
|
Hedges’ correction |
.4369 |
.286 |
.036 |
.534 |
||
|
a. The denominator used in estimating the effect sizes. Cohen’s d uses the sample standard deviation of the mean difference. Hedges’ correction uses the sample standard deviation of the mean difference, plus a correction factor. |
Part 2
|
Group Statistics |
||||||
|
Status at Ten Years |
||||||
|
Serum Cholesterol 58 — Mg per DL |
Alive |
179 |
264.87 |
52.981 |
3.960 |
|
|
Dead |
61 |
261.80 |
51.807 |
6.633 |
|
Independent Samples Test |
|
Independent Samples Effect Sizes |
||||
|
52.687 |
.058 |
-.233 |
.349 |
|
|
52.854 |
-.232 |
.348 |
||
|
Glass’s delta |
.059 |
.350 |
||
|
a. The denominator used in estimating the effect sizes.
Cohen’s d uses the pooled standard deviation. Hedges’ correction uses the pooled standard deviation, plus a correction factor. Glass’s delta uses the sample standard deviation of the control group. |
Part 3
|
ANOVA |
||||
|
Respondent’s income; ranges recoded to midpoints |
||||
|
Sum of Squares |
Mean Square |
F |
||
|
Between Groups |
69070941438.459 |
2 |
34535470719.230 |
68.102 |
|
Within Groups |
463504108043.547 |
914 |
507116091.951 |
|
|
Total |
532575049482.007 |
916 |
POST HOC Test
|
Multiple Comparisons |
||||||||||||
|
Dependent Variable: Respondent’s income; ranges recoded to midpoints |
||||||||||||
|
Bonferroni |
||||||||||||
|
(I) Degree |
(J) Degree |
Mean Difference (I-J) |
Std. Error | |||||||||
|
Lower Bound |
Upper Bound |
|||||||||||
|
Less than high school |
High school |
– 9006.727* |
2397.441 |
.001 |
– 14756.74 |
– 3256.72 |
||||||
|
Junior college or more |
– 24252.154* |
2474.337 |
– 30186.59 |
– 18317.72 |
||||||||
| 9006.727* | 3256.72 | 14756.74 | ||||||||||
|
– 15245.427* |
1601.619 |
– 19086.74 |
– 11404.11 |
|||||||||
| 24252.154* | 18317.72 | 30186.59 | ||||||||||
| 15245.427* | 11404.11 | 19086.74 | ||||||||||
|
*. The mean difference is significant at the 0.05 level. |
Running Head:
PARAMETRIC TESTING 2
RES814-1902C-03
Quantitative Research Methods
Parametric Testing
Brett Dagel
Colorado Technical University
Instructor: Dr. Charles P. Kost
Date: 5/15/2019
PARAMETRIC TESTING 2
Parametric Testing
Part 1:
T-Test
In part 1 of this statistical analysis, the idea is to compare the productivity levels of two separate management styles, and they are traditional vertical management (TVM) and autonomous work teams (AWT). A paired-samples t-test was run to analyze this situation and to see which type of management style creates higher production levels. There is a sample population of (N
= 100) workers in this study. These individuals were first evaluated using TVM methods, and then the company used the same people and analyzed their production levels after switching to the AWT system (CTU Online, 2019). The hypotheses in this situation are that the null hypothesis will show that there are no significant differences between the two group’s productions levels and the alternative hypothesis will demonstrate that there are pre and post differences that exist. Table 1 demonstrates the production levels as having an increase of approximately 8 points and that the SD went down about 7 points. The pre-change levels of production are (M = 76.83, SD = 16.94), and the post-change productions levels are (M = 84.80, SD = 9.76). These numbers help to show that the TVM system produced lower production values than that of the newer AWT system. Overall, the data tells us that the worker’s productions levels increased under the AWT method with less deviation (Miller, n.d.).
Table 1
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
productivity level preceding the new process
76.83
100
16.936
1.694
productivity level following the new process
84.80
100
9.757
.976
The second part of step one is a paired-samples t-test, otherwise known as a 2-tailed student t-test (Miller, n.d.). The significant difference for this test got set at a level of 0.05 or less. If these parameters are met, then the null hypothesis can get rejected. According to the calculated data in Table 3, the analysis of the chance probability, or the 2-tailed significance value is less than our set level of 0.05, allowing us to reject the null hypothesis in this situation. We can then use the alternative hypothesis and say that there is a significant difference between pre and post-implementation production levels (Miller, n.d.).
Table 2
Paired Samples Test
Paired Differences
t
df
Sig. (2-tailed)
Mean
Std. Deviation
Std. Error Mean
95% Confidence Interval of the Difference
Lower
Upper
Pair 1
productivity level preceding the new process – productivity level following the new process
-7.970
19.090
1.909
-11.758
-4.182
-4.175
99
.000
Part 2:
T-Test
The focus of part 2 of this individual project attempts to figure out if people are alive or dead ten years after a coronary incident and compare their health status to their diastolic blood pressure (DBP) that got taken at the time of the event. The primary goal of this study is to compare these two elements to see if these individuals had significant differences in the DBP and correlate those finding with whether each of these people is alive or dead within ten years (CTU Online, 2019). The null hypothesis for this study is that there is not a difference between the person’s DBP and their mortality after ten years. The alternative hypothesis should then state that there are significant differences that exist between the DBP and their ten-year mortality.
In Table 3, there is a population that is equal to (N = 239) individuals. The mean of DBP of those who have died is approximately five points lower than that of those who are still alive, and their SD is about 5 points less. These stats are (M = 93.35, SD = 16.73) for the people who are living and (M = 87.79, SD = 11.41) for those who have passed away. This finding helps to indicate that those who have died after the ten years had a smaller variation in their DBP than those who are still alive (Miller, n.d.).
Table 3
Group Statistics
Status at Ten Years
N
Mean
Std. Deviation
Std. Error Mean
Average Diast Blood Pressure 58
Alive
60
93.35
16.731
2.160
Dead
179
87.79
11.409
.853
Table 4 represents an independent sample t-test ran for the same pair of variables. After evaluating the data, we can see that the two-tailed significance values are not equal. So, if equal variances are not assumed, and with the standard level again set at 0.05 or less, we can reject the null hypothesis because the significance value of the “not assumed” row equals 0.02. Moreover, we can accept the alternative hypothesis that states there are significant differences between the population’s DBPs and the people that are alive and those who have died (Miller, n.d.).
Table 4
Independent Samples Test
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
Average Diast Blood Pressure 58
Equal variances assumed
10.944
.001
2.879
237
.004
5.557
1.930
1.754
9.360
Equal variances not assumed
2.393
78.197
.019
5.557
2.322
.934
10.180
Part 3
In part 3 of the individual project, we look to examine the relationship that exists between someone’s income and their level of happiness. The level of happiness will have three tiers, and they are; not too happy, pretty happy, and very happy (CTU Online, 2019). Since there are multiple levels of evaluation, we must incorporate two pairs of hypotheses. The first null hypothesis will state that there is no real difference between happiness levels and income levels, with an alternative hypothesis that states there are significant differences between happiness levels and income levels. The next null hypothesis is that there are no substantial differences between various pairs of income levels and happiness levels with an alternative hypothesis stating that there are differences between the various pairs of income levels and happiness levels.
Table 5 helps to demonstrate the ANOVA. The statistical significance shown in the table is well below the 0.05 level which allows us to reject the first null hypothesis and use the alternative conclusion that states there is a substantial statistical difference that exists between someone’s income level and their level of happiness (Miller, n.d.).
Table 5
ANOVA
Respondent’s income; ranges recoded to midpoints
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
11684958520.000
2
5842479261.000
10.478
.000
Within Groups
500706851000.000
898
557580012.200
Total
512391809500.000
900
Post Hoc Tests
Finally, we move onto the Post Hoc Bonferroni test. Table 6 compares the levels of happiness to one another. As we evaluate the significance value for all types of happiness, we can see that all levels demonstrate values less than the set value of 0.05 allowing us to reject the second null hypothesis for all three tiers of happiness. We can then accept the second alternative hypothesis and state that there are significant differences between the various pairs of income levels and happiness levels (Miller, n.d.). Moreover, we can make the general conclusion that there is a positive correlation between someone’s income and their level of happiness. Or, in other words, someone with a low income often records a lower level of happiness, and those with more money tend to be happier. This statement is not always accurate and may not always be true as there could be individuals with large incomes who are unhappy and those with small incomes who are happy (Miller, n.d.).
Table 6
Multiple Comparisons
Dependent Variable: Respondent’s income; ranges recoded to midpoints
Bonferroni
(I) GENERAL HAPPINESS
(J) GENERAL HAPPINESS
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
VERY HAPPY
PRETTY HAPPY
4352.726*
1745.264
.038
166.76
8538.70
NOT TOO HAPPY
13090.621*
2900.801
.000
6133.12
20048.12
PRETTY HAPPY
VERY HAPPY
-4352.726*
1745.264
.038
-8538.70
-166.76
NOT TOO HAPPY
8737.895*
2729.327
.004
2191.67
15284.11
NOT TOO HAPPY
VERY HAPPY
-13090.621*
2900.801
.000
-20048.12
-6133.12
PRETTY HAPPY
-8737.895*
2729.327
.004
-15284.11
-2191.67
*. The mean difference is significant at the 0.05 level.
References
CTU Online. (2019). Parametric analysis and non-parametric analysis. Retrieved May 14, 2019,
from
https://studentlogin.coloradotech.edu/UnifiedPortal/3/6#/class/181725/assignment/14256″ https://studentlogin.coloradotech.edu/UnifiedPortal/3/6#/class/181725/assignment/14256
82
Miller, R. (n.d.). Week 6: Parametric tests. [Video file]. Retrieved from
http://breeze.careeredonline.com/p7xq8uo99cm/