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Data Analysis: Hypothesis Testing

Data analysis is recognized as the critical step of the overall research process to make better inferences about the research project. It is noteworthy to indicate that independent samples t test, dependent samples (paired samples) t test, and ANOVA are recognized as major statistical forms to characterized existing association between different variables ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"CEqJp83D","properties":{"formattedCitation":"(Creswell, 2014)","plainCitation":"(Creswell, 2014)","noteIndex":0},"citationItems":[{"id":235,"uris":["http://zotero.org/users/local/qLzeF6Hj/items/ATDAVR9L"],"uri":["http://zotero.org/users/local/qLzeF6Hj/items/ATDAVR9L"],"itemData":{"id":235,"type":"book","ISBN":"978-1-4522-2610-1","publisher":"SAGE Publications","title":"Research Design: Qualitative, Quantitative, and Mixed Methods Approaches","URL":"https://books.google.com.pk/books?id=4uB76IC_pOQC","author":[{"family":"Creswell","given":"J. W."}],"issued":{"date-parts":[["2014"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Creswell, 2014). This form of consideration is vital to correctly identify the trend of variables considered for the research study ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"G5pNpJXh","properties":{"formattedCitation":"(Ngulube, 2019)","plainCitation":"(Ngulube, 2019)","noteIndex":0},"citationItems":[{"id":236,"uris":["http://zotero.org/users/local/qLzeF6Hj/items/XDCD49YQ"],"uri":["http://zotero.org/users/local/qLzeF6Hj/items/XDCD49YQ"],"itemData":{"id":236,"type":"book","ISBN":"978-1-79981-472-6","publisher":"IGI Global","title":"Handbook of Research on Connecting Research Methods for Information Science Research","URL":"https://books.google.com.pk/books?id=RsO4DwAAQBAJ","author":[{"family":"Ngulube","given":"P."}],"issued":{"date-parts":[["2019"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Ngulube, 2019). The data set for the research project of Sun Coast Remediation is used to practically apply and analyze the statistical tests of independent samples t test, dependent samples (paired samples) t test, and ANOVA. These tests are used to determine the suitability of the hypothesis constructed by researcher for this specific project ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"XlvKA368","properties":{"formattedCitation":"(Nickerson, 2000)","plainCitation":"(Nickerson, 2000)","noteIndex":0},"citationItems":[{"id":368,"uris":["http://zotero.org/users/local/qLzeF6Hj/items/5N476BRF"],"uri":["http://zotero.org/users/local/qLzeF6Hj/items/5N476BRF"],"itemData":{"id":368,"type":"article-journal","container-title":"Psychological methods","issue":"2","page":"241","title":"Null hypothesis significance testing: a review of an old and continuing controversy.","volume":"5","author":[{"family":"Nickerson","given":"Raymond S."}],"issued":{"date-parts":[["2000"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Nickerson, 2000).

Independent Samples t Test: Hypothesis Testing

Ho4: There is no statistically significant difference in mean values for the DV between Group A (Prior Training Scores) and Group B (Revised Training Scores).

Ha4: There is a statistically significant difference in mean values for the DV between Group A (Prior Training Scores) and Group B (Revised Training Scores).

t-Test: Two-Sample Assuming Unequal Variances

Group A Prior Training Scores

Group B Revised Training Scores

Mean

69.79032258

84.77419355

Variance

122.004495

26.96456901

Observations

62

62

Hypothesized Mean Difference

0

df

87

t Stat

-9.666557191

P(T<=t) one-tail

9.69914E-16

t Critical one-tail

1.662557349

P(T<=t) two-tail

1.93983E-15

t Critical two-tail

1.987608282

The central aim of conducting independent samples t test is to successfully compares the means of two independent groups to statistically determine whether population means of two groups are significantly different or not ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"I3Hkf6OO","properties":{"formattedCitation":"(Bakker & Wicherts, 2014)","plainCitation":"(Bakker & Wicherts, 2014)","noteIndex":0},"citationItems":[{"id":366,"uris":["http://zotero.org/users/local/qLzeF6Hj/items/3B3JV44A"],"uri":["http://zotero.org/users/local/qLzeF6Hj/items/3B3JV44A"],"itemData":{"id":366,"type":"article-journal","container-title":"Psychological methods","issue":"3","page":"409","title":"Outlier removal, sum scores, and the inflation of the type I error rate in independent samples t tests: The power of alternatives and recommendations.","volume":"19","author":[{"family":"Bakker","given":"Marjan"},{"family":"Wicherts","given":"Jelte M."}],"issued":{"date-parts":[["2014"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Bakker & Wicherts, 2014). The means values for both the groups are different as this value (69.790) for group A is less than the mean value of group B (84.7741). The results for this test provides information to establish existing difference between two independent groups of prior training scores and revised training scores for the 62 observations. The alpha value for this test is set as 0.05 that is established as benchmark to determine the significance of p value ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"7vkKGlxv","properties":{"formattedCitation":"(Rochon, Gondan, & Kieser, 2012)","plainCitation":"(Rochon, Gondan, & Kieser, 2012)","noteIndex":0},"citationItems":[{"id":367,"uris":["http://zotero.org/users/local/qLzeF6Hj/items/IERQPDXV"],"uri":["http://zotero.org/users/local/qLzeF6Hj/items/IERQPDXV"],"itemData":{"id":367,"type":"article-journal","container-title":"BMC medical research methodology","issue":"1","page":"81","title":"To test or not to test: Preliminary assessment of normality when comparing two independent samples","volume":"12","author":[{"family":"Rochon","given":"Justine"},{"family":"Gondan","given":"Matthias"},{"family":"Kieser","given":"Meinhard"}],"issued":{"date-parts":[["2012"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Rochon, Gondan, & Kieser, 2012). The outcomes of the study show that the mean value for Group A is lower as compare to Group B. Moreover, the results for p value of two tail also helps to identify the overall significance of the hypothesis development. The outcome for the indicator of p value shows that p value (1.939) is greater than alpha value (.05). This result clearly shows that the null hypothesis is accepted that means that there is no statistically significance difference in mean values of the DV between Group A and Group B.

Dependent Samples (Paired Samples) t Test: Hypothesis Testing

Ho5: The true mean difference between the paired samples of (Pre-Exposure) and (Post-Exposure) is equal to zero.

Ha5: The true mean difference between the paired samples of (Pre-Exposure) and (Post-Exposure) is not equal to zero.

t-Test: Paired Two Sample for Means

Pre-Exposure μg/dL

Post-Exposure μg/dL

Mean

32.85714

33.28571429

Variance

150.4583

155.5

Observations

49

49

Pearson Correlation

0.992236

Hypothesized Mean Difference

0

df

48

t Stat

-1.9298

P(T<=t) one-tail

0.029776

t Critical one-tail

1.677224

P(T<=t) two-tail

0.059553

t Critical two-tail

2.010635

The results for this study are helpful to better determine about the mean difference of paired samples for the selected groups. The results based on the consideration of 49 observations for the paired samples of Pre-Exposure and Post-Exposure. The results for this analysis is interesting because p value for the two tail domain is equal to the level of significance (0.05). This result helps researcher to accept the null hypothesis of this study that means that the true mean value between paired samples is equals to the value of zero.

ANOVA: Hypothesis Testing

Ho6: Mean value for all the four groups (Air, Soil, Water, Training) is the same

Ha6: Mean value for all the four groups (Air, Soil, Water, Training) is not the same

Anova: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

A = Air

20

178

8.9

9.357895

B = Soil

20

182

9.1

3.042105

C = Water

20

140

7

6.631579

D = Training

20

108

5.4

1.410526

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

182.8

3

60.93333

11.9231

1.76E-06

2.724944

Within Groups

388.4

76

5.110526

Total

571.2

79

The results of ANOVA test explicitly show that p-value (1.76) for this analysis is greater than the level of significance (0.05). This form of consideration helped to determine that null hypothesis for this analysis is accepted ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"HPqdAMZF","properties":{"formattedCitation":"(Cuevas, Febrero, & Fraiman, 2004)","plainCitation":"(Cuevas, Febrero, & Fraiman, 2004)","noteIndex":0},"citationItems":[{"id":365,"uris":["http://zotero.org/users/local/qLzeF6Hj/items/TABTV5B8"],"uri":["http://zotero.org/users/local/qLzeF6Hj/items/TABTV5B8"],"itemData":{"id":365,"type":"article-journal","container-title":"Computational statistics & data analysis","issue":"1","page":"111-122","title":"An anova test for functional data","volume":"47","author":[{"family":"Cuevas","given":"Antonio"},{"family":"Febrero","given":"Manuel"},{"family":"Fraiman","given":"Ricardo"}],"issued":{"date-parts":[["2004"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Cuevas, Febrero, & Fraiman, 2004). In other words, it is established that the mean value for the groups is same.

References

ADDIN ZOTERO_BIBL {"uncited":[],"omitted":[],"custom":[]} CSL_BIBLIOGRAPHY Bakker, M., & Wicherts, J. M. (2014). Outlier removal, sum scores, and the inflation of the type I error rate in independent samples t tests: The power of alternatives and recommendations. Psychological Methods, 19(3), 409.

Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. Retrieved from https://books.google.com/books?id=4uB76IC_pOQC

Cuevas, A., Febrero, M., & Fraiman, R. (2004). An anova test for functional data. Computational Statistics & Data Analysis, 47(1), 111–122.

Ngulube, P. (2019). Handbook of Research on Connecting Research Methods for Information Science Research. Retrieved from https://books.google.com/books?id=RsO4DwAAQBAJ

Nickerson, R. S. (2000). Null hypothesis significance testing: A review of an old and continuing controversy. Psychological Methods, 5(2), 241.

Rochon, J., Gondan, M., & Kieser, M. (2012). To test or not to test: Preliminary assessment of normality when comparing two independent samples. BMC Medical Research Methodology, 12(1), 81.