Discussion Replies: Chi-Square, Strength, and Relationships Between Variables

Herve Ngate

Discussion Week 5: Chi-Square, Cross Tabulation, and Non-parametric Association

 

D.5.7.1 In Output 7.1:

(a) What do the terms “count” and “expected count” mean?

In Output 7.1, the term “count” refers to the number of cases measured or observed during data collection, while the term “expected count” indicates the results after computing data collected.

(b) What does the difference between them tell you?

According to Morgan et al. (2020), the difference between the “expected count” and the “count” demonstrates that the Chi-Square Tests must clarify if the discrepancies are systematic and find out if the relationship between variables is statistically significant.

D.5.7.2 In Output 7.1:

(a) Is the (Pearson) chi-square statistically significant? Explain what it means.

The asymptotic significance of the Pearson Chi-Square for two-sided shows the value of .056, indicating it is not statistically significant. Morgan et al. (2020) interpreted it as the fact that there is no certainty that the difference between fast and regular track is systematic in the student’s grades.

(b) Are the expected values in at least 80% of the cells ≥ 5? How do you know? Why is this important?

The  Crosstabulation table shows that the minimum expected count is 14.1, indicating that more than 80% of the cells have an expected frequency ≥ 5. It is crucial because the number of expected counts will determine the use of the Pearson Chi-Square or Fisher’s exact test. When the expected count is at least 5, the Pearson Chi-Square is used, but Fisher's exact test is used if it is less than five (Morgan et al., 2020).

D.5.7.3 in Output 7.2:

(a) how is the risk ratio calculated? What does it tell you?

The risk ratio is calculated by dividing the percentage of students who did not take  algebra 2 by the percentage of students who did (Morgan et al., 2020). For example, the first risk ratio of 1.531 =70%/45.7% indicates that students with  low math grades were 1.5 times likely or not to take  algebra 2. The second risk ratio of .533=30%/54.3% demonstrates that the students with  high math grades were ½ times more likely or not to take  algebra 2.

(b) how is the odds ratio calculated, and what does that tell you?

The odds ratio is calculated by dividing the ratio with the highest value by the one with the lowest. For example, the OR of 2.77 = 1.531/.553. This number shows that “the odds of failing to take  algebra 2 are 2.77 times higher for those with low math grades than for those with high math grades" (Morgan et al., 2020, p.144).

(c) how could information about the odds ratio be useful to people wanting to know the practical importance of research results?

The odds ratio provides important information on the relationship's strengths between two nominal variables. People who want to know the practical importance of the research results could use the odds ratio to decide which variable to focus on and which one to disregard to measure the effectiveness of their studies.

(d) what are some of the limitations of the odds ratio as an effect size measure?

The odds ratio as an effect size measure seems to apply only to a limited number of fields like healthcare and prevention science. Therefore, a more significant number of industries might not be interested in using it. In addition, the odds ratio poses the challenge of deciding what represents a big ratio (Morgan et al., 2020), considering that cases could be complex to find or too famous for some studies.

D.5.7.4 Because father’s and mother’s education revised are 3-level variables with at least ordinal data, which of the statistics used in Problem 7.3 is the most appropriate to measure the strength of the relationship: phi, Cramer’s V, or Kendall’s tau-b? Interpret the results. Why are tau-b and Cramer’s V different?

Morgan et al. (2020) posit that Kendall’s tau-b is most appropriate to measure the strength of the relationship between father’s and mother’s education because both variables are ordered. The Symmetric measures show that tau’s value is less than .001, indicating a statistically positive association between father’s and mother’s education. This could be interpreted as highly educated parents marrying each other and less educated parents marrying among themselves.

Tau-b considers variables ordered to measure the relationship's strengths among variables, whereas Cramer’s V will be effective only if variables are nominals with three or more levels.

D.5.7.5 In Output 7.4:

(a) How do you know which is the appropriate value of eta?

The  Directional Measures show two values of eta: One for math courses taken with a value of .328 and one for academic track with a value of .419. The appropriate value of eta would be .328 because math courses taken as a dependent variable are the ones being viewed (Morgan et al., 2020).

(b) Do you think it is high or low? Why?

SPSS computes eta from zero to 1 (Morgan et al., 2020). Therefore, the eta value of .328 is relatively low even if it confirms an association between  math courses taken and  academic track.

(c) How would you describe the results?

The results could be described as “those in the fast track were more likely to take several or all the math courses than those in the regular track” (Morgan et al., 2020, p.149).

 

 References

Morgan, G. A., Leech, N., Gloeckner, G., & Barrett, K. C. (2020). IBM SPSS for introductory statistics: Use and interpretation (6th ed.). Routledge.