Miller_U6
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Jan 9, 2024
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Uploaded by gregmiller
Non-Parametric Models
by
John Gregory Miller
Capella University
Presented in Partial Fulfillment
Of the Requirements, of
BMGT8034: Quantitative Research Techniques
503 Lafayette Street
Pittsburg, TX, 75686
Telephone: 903-399-6100
Email: jmiller316@capellauniversity.edu
Instructor: Dr. Brock Boudreau
State the research questions and associated null and alternative hypotheses. Verify assumptions associated with the non-parametric statistical test.
Report correct hypothesis testing results. Identify all key limitations and draw conclusions
Step A: Questions and Hypotheses
Begin your project by developing a solid foundation to guide the study.
1.
Develop a research question appropriate for the Mann-Whitney test.
Q1 Would people accept lower offers and propose higher offers when listening to music that they like? 2.
State the null and alternative hypotheses appropriate for a Mann-Whitney test.
H0 – Null – The distribution of Offers Made is the same across categories of Background Music.
H1 There is no significate difference in the distribution of Offers Made is the same across categories of Background Music H2 There is a significate difference in the distribution of Offers Made is the same across categories of Background Music
3.
Identify the level of measurement for each variable (such as nominal, ordinal, interval, or ratio).
Ordinal - When categories are ordered, the variable is known as an ordinal
variable
. Ordinal
data tell us not only that things have occurred, but also the order in which they occurred. However, these data tell us nothing about the differences between values.
4.
Using the decision tree in the back of your Field textbook, describe the selection process for the Mann-Whitney test used in this assignment. When you want to compare the distributions in two conditions and these conditions contain different entities, then you have two choices: the Mann–Whitney test (Mann & Whitney, 1947) and Wilcoxon's rank-
sum test (Wilcoxon, 1945). Both tests are equivalent, and there's another Wilcoxon test, which gets extremely confusing. These tests are
the non-parametric equivalent of the independent t-test, which we'll discover in Chapter 9.
Two samples,
To determine if the populations
Independent t-test
Mann-Whitney
between subjects
of two independent samples U test
5.
Identify the significance level (alpha) for the test.
While the exact significate level for this test is .074, the reported significance level is .05.
Step B: Test the Assumptions
While non-parametric tests are sometimes called “assumption-free tests” (Field, 2013, p. 214), we still test for normality and homogeneity of variance. In fact, the results of these tests and our inability to fix the issues are why we end up conducting non-parametric tests
.
1.
Identify and address any missing data, oddly coded data, and outliers.
2.
Identify and test the assumptions (for example, normality and homogeneity of variance) using SPSS.
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3.
Create the appropriate graphs for visual analysis of the assumptions.
4.
Analyze the results of the tests, address any issues, and state your conclusions for each assumption.
Note:
Review the Field textbook, Chapter 5, "The Beast of Bias" and videos for more on how to complete this step.
Step C: Run the Test and Results
1.
Explore the data and relationships by creating the appropriate graphs for visual analysis.
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2.
Test the null hypothesis using a Mann-Whitney test and report the results.
3.
Analyze and interpret the results and make a decision whether to reject the hypothesis.
4.
Justify your decision and describe what it means.
In this discussion, we will carry out a Mann–Whitney test because we want to compare scores in two independent samples: participants who listened
to Bon Scott vs. those who listened to Brian Johnson to see whether there was a significant difference between offers made.
It will be important to report effect sizes so that people have a standardized measure of the size of the effect you observed, which they can compare to other studies. SPSS doesn't calculate an effect size for us, but we can calculate approximate effect sizes thanks to the fact that SPSS converts the test statistics into a z
-score. The equation to convert a z
-score into the effect size estimate, r
, as follows:
(Field, 2013)
Calculating the Effect Size for this test we would substitutes the following information to get the effect size:
r - is the comparison we are testing against
z – Standardized Test Statistic – 1.850
N – Total N – 36
The resulting equation will be as follows:
rBonScott
−
Brian Johnson
=
1.850
√
36
=
.31
This represents a medium effect that when listening to Brian Johnson people proposed higher offers than when listening to Bon Scott, suggesting that they preferred Brian Johnson to Bon Scott. “Cohen has made some widely used suggestions about what constitutes a large or small effect: d = 0.2 (small), 0.5 (medium) and 0.8 (large)” (Field, 2013, p. 80). However, this effect was not significant because the a fairly substantial effect size can still be non-significant in a small sample. Because the Offers made by people listening to Bon Scott (Median = 3.0) were not significantly different from offers by people listening to Brian Johnson
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(Median = 4.0), You’ll can get these values by running Analyze > Descriptive Statistics > Explore
.
The follow information will be the results for the data sampled: U = 218.50, z = 1.85, p = .074, r = .31.
Step D: Limitations and Conclusions
1.
Compute and analyze the statistical power using G*Power.
2.
Identify and describe the implications of the limitations from Steps A, B, and C.
3.
Interpret the results and draw conclusions. Describe what the results of
the test mean, considering the limitations.