Application: SPSS Exercise

Introduction

The exercises for this week required that the student compute a chi-square test as well as a nonparametric test of some hypothesis. The exercises in this paper are on page 328, 343 and 354 from the SPSS textbook by Salkind and Green. In these exercises, the learner demonstrates the understanding and experience gained from class on conducting Mann-Whitney tests and chi-square tests on a given sample. Chi-square tests are very helpful when it comes to qualitative groupings where we want to have one or more categories (Green & Salkind, 2011).The chi-square test will take place to find out if potato chips test better when fried using canola oil, animal fat or baked. The second Mann-Whitney test was on finding out the correlation between hair color and social extroversion. The non-parametric test is, however, possesses lower statistical influence compared to the corresponding parametric procedure (Boslaugh & Watters, 2008).

PG 328: Exercise 1-4 (Chi-square test)

The observed frequency for one sample t-test

Method of cooking potato chips
	Observed N	Expected N	Residual
Fried in animal fat	7	16.0	-9.0
Fried in Canola oil	33	16.0	17.0
Baked	8	16.0	-8.0
Total	48

The table above shows that a significant value exists at for X2 (2, N = 48), and it is 27.13. The means that the observed frequency of chips fried in canola oil of 33 exceeds the values of the anticipated frequency that is 16. On the other hand, the observed frequency of chips fried using animal fat is seven while the one for baked was 8 (n = 8). These values are less than the anticipated frequency that is 16. Below is a follow-up one-sample chi-square test to demonstya5trateb the results are not dependent on the type of cooking using varying proportions.

Number who preferred each type of chip
	Observed N	Expected N	Residual
7	7	16.0	-9.0
8	8	16.0	-8.0
33	33	16.0	17.0
Total	48

The above table demonstrates that the indvidualst6ahqt preferred chips cooked with canola oil and those who preferred the chips fried with animal fat vary greatly. The chance value of the former is 0.33 while the chance value for the latter is 0.67. The value of X2 as per the results is also 27.12, and the p value is less than 0.01 (P<0.01). The value of x calculated is the one that occurs at X2 (1, N = 48). From the result, we can conclude that individual prefer the chips fried using canola oil rather than animal fat or baked. We can present the results graphically as in the following figure.

Page 343 exercise 1-4: Mann-Whitney U test

Test Statistics
	Time in Seconds
Mann-Whitney U	28.000
Wilcoxon W	83.000
Z	-3.811
Asym. Sig. (2-tailed)	.000
Exact Sig. [2*(1-tailed Sig.)]	.000b
a. Grouping Variable: weight
b. Not corrected for ties.

The table analyzes the p-values were two of them serve as reported values. One is a two-tailed where no correction for ties takes place while the other is two-tailed that entails correction for ties and has a basis of Z approximation. The hypothesis for the test was to find out the time spent eating Big Mac meals between the individuals of overweight and those with normal weight. Those individuals for overweight have a mean eating time of 8.30 while the ones with normal weight have a mean eating time of 24.57 as shown by the findings. The results of the Mann-Whitney U-test reveals that those individuals with overweight eat more hastily compared to individuals of normal weight. I compared the p-values of the Mann-Whitney with those for an independent t-test shown in the above table. The value of z = -3.81 and the value for p<0.01. Let us compute the mean eating time ranks for the above case.

Ranks
	weight	N	Mean Rank	Sum of Ranks
Time in Seconds	Over weight	10	8.30	83.00
	Normal weight	30	24.57	737.00
	Total	40

We can also represent these results graphically as shown below using a boxplot. That provides a clearer understanding of the distributions of the two groups of individuals.

Ranks
	Social Extroversion	N	Mean Rank
Hair Color	1	1	15.50
	2	5	11.90
	3	4	9.50
	4	2	12.50
	5	4	6.50
	6	1	3.50
	10	1	3.50
	Total	18

The results from the above table show that there is a significant value at 0.05 with X2 at 2 and N = 18 giving us 5.96, the p-value is 0.051. The hair color variable has the value of 0.35, and this supports the null hypothesis that a correlation exists between hair color and social extroversion. We can also conduct the frequencies to determine the validity and reliability of the above results and the descriptive table is as shown below.

The frequencies table

Frequencies
		Social Extroversion
		1	2	3	4	5	6	7	8	9	10
Hair Color	> Median	1	3	1	1	0	0	0	0	0	0
	<= Median	0	2	3	1	4	1	0	0	0	1

The table demonstrates the effect size of the population on the sample size. A small sample size does not give a true picture of the actual results, and it may differ greatly from the actual result of the phenomenon being tested. If we have to have a clear picture of the hypothesis test, we have to carry out further follow-up test with a larger sample size. That will help us find a more accurate result of the correlation between hair color and social extroversion. We can see that the value of p is 0.02 and X2(2, N = 40). All the anticipated frequencies are less than five.  analyzes.

One-way ANOVA test

ANOVA
Hair Color
	Sum of Squares	Df	Mean Square	F	Sig.
Between Groups	5.300	6	.883	1.450	.280
Within Groups	6.700	11	.609
Total	12.000	17

From the one-way ANOVA test, we see that the mean square within groups is 0 .883 during the mean square within the groups 0 .609.  The one-way ANOVA test results show that there is a considerable main effect for support type, F (2, 17) = 1.45, p < .05, and partial η2 = .35. There is no significant effect for the groups but a significant level between the groups occurs at point 0.28. Comparing the results from the Mann-Whitney and the ANOVA shows that there is a positive correlation between hair color and social extroversion.

Conclusion

Chi-square tests and nonparametric studies are vital in helping have a clear picture on hypothesis test when carrying out a quantitative study. However, one-sample chi-square tests do not recognize the quantitative differences that may exist among the difference categories of variables (Laureate Education, 2009). When we supplement it with nonparametric tests, then we can achieve the validity and reliability of the result. That is because reliability can only occur when we can carry out a follow-up test and get similar results. The tests on the samples given helped to find a clear understanding of the hypotheses being tested.

References

Boslaugh, S. & Watters, P. A. (2008). Research design. Statistics in a nutshell. Sebastopol, CA: O'Reilly Media.

Green, S. B. & Salkind, N. J. (2011). Using SPSS for windows and macintosh: Analyzing and understanding data (6th ed.). Upper Saddle River, NJ: Prentice Hall

Laureate Education (Producer). (2009). Nonparametric statistics: The chi-square test [Video file]. 

Sherry Roberts is the author of this paper. A senior editor at MeldaResearch.Com in College Essay Writing Service if you need a similar paper you can place your order from cheap essay help online.