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Quantitative Research Methods Week 5
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Tutor’s Name
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D.5.7.1
D.5.7.1.a
The Count represents a particular frequency that is observed in a specific cell of the
crosstab tabular presentation. On the other hand, the expected Count represents the predicted
frequency under a specific cell provided, assuming that the null hypothesis is accepted.
D.5.7.1.b
The Count represents the number of people, with the Phi or Kramer representing the
expected counts. The difference between Count and Expected Count represents whether the
variables are dependent or independent. With the two variables independent, the distribution
between the observations will be similar among the first and second variables.
D.5.7.2
D.5.7.2.a
Based on the cross-tabulation analysis, the output includes math grades, Chi-Squared, and
symmetric measure tables. According to the results obtained from the Pearson Chi-Squared, the
resultant P-value is 0.0056 (Leech et al, 2005). According to the rejection rule, the null
hypothesis is rejected the p-value is less than 0.05. Since 0.056 is greater than 0.05, a conclusion
can be made that there is no significant relationship between gender and expected Math grades.
D.5.7.2.b
According to Chi-Square guideline tests, at least 80% of the cross-tabular cells should
have expected frequency ranges of 5 or more than 5. Otherwise, the assumption of expected
frequency would be contradicted. Consequently, before running any Chi-Square test, the law of
expected frequency must be tested and verified. In every Chi-Square table, the footnotes indicate
that every cell in the cross table has values greater or equal to 5 (≥ 5) consequently, one can
conclude that in at least 80% of the Cross-table cells, the expected values are equal to or greater
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than 5 (Morgan et al., 2013). An analysis of the Math grades and gender cross-tabulation reveals
that the expected counts for most A-B females, Male Less A-B, and most A-B males are
16.9,19.9,14.1, and 24.1; all these values are greater than 5, and as such, the expected frequency
law holds.
D.5.7.4
With the variables explaining father and mother education level representing ordinal data,
The Kendall-Tau method is the most suitable measure to illustrate the relationship between the
variables. In Kendall- tau analysis, the fundamental assumption for the measure to hold is that
the data presented should be ordinal. Using Kendall Tau measure, an analysis of the reported
statistical significance indicates a strong association between Fathers and mothers with a 0.572
P-value < 0.001 (Morgan et al., 2013). The significance indicates a high relationship between
education and marriage, with highly educated fathers preferring to settle with highly educated
mothers. The story is the same with lowly educated fathers marrying less educated mothers.
D.5.7.3
With the data in ordinal form, The Kendall Tau Test is the most suitable measure to
explain the strength of this particular relationship. The difference in Crammer V and Kendall
Tau is based on the type of data presented for analysis. In cases where the data in question is
gauged at a nominal level, the Crammer's V method is the most suitable; however, for ordinal
data where the strength between two variables is assessed, the Kendal Tau measure remains the
most suitable method to use.
D.5.7.5
D.5.7.5.a
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The appropriate value of Eta is 0.328 since the Math Courses undertaken represent
dependent variables
D.5.7.5.b
The eta in question ranges from medium to large effect size. Since Eta squared would
represent a shared 11% significance, The Eta is high.
D.5.7.5.c
Eta is used to test the relationship's strength between academic track record and the math
courses undertaken (Eta =33%). Eta 33% represents a medium-large size effect; consequently, it
is evident that the participants in the fast track were more likely to undertake Math courses than
the participants in regular tracks.
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References
Leech, N., Barrett, K. C. Morgan, G. A. (2005). SPSS for Intermediate Statistics; Use and
Interpretation. Lawrence Erlbaum Associates, Inc.: Mahwah, NJ.
Morgan, G. A., Leech, N., Gloeckner, G., Barrett, K. C. (2013). IBM SPSS for introductory
statistics (5th Ed.). Routledge: New York, NY
