Please respond to the 4 discussion post below in 250 words or more. The reply mu

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Please respond to the 4 discussion post below in 250 words or more. The reply mu

Please respond to the 4 discussion post below in 250 words or more. The reply must summarize the
student’s findings and indicate areas of agreement, disagreement, and improvement. It must be
supported with scholarly citations in the latest APA format and corresponding list of references.
1. Kandice
D.5.7.1 In Output 7.1: (a) What do the terms “count” and “expected count” mean? (b) What does the difference between them tell you?
D.5.7.1(A) The term count means the amount and or number of subjects that are within a cell, and expected count means what is expected to be found within the cell based upon the marginal totals.
D.5.7.1(B) Some difference between observed and expected counts tells us that within any randomized group of participants, notable variances could indicate a systematic difference. Statistics such as chi-square tests are used to determine if discrepancies that exist between expected and observed counts are statistically significant, or bigger than might be expected to occur by chance (Morgan et al., 2020)
D.5.7.2 In Output 7.1: (a) Is the (Pearson) chi-square statistically significant? Explain what it means. (b) Are the expected values in at least 80% of the cells ≥ 5? How do you know? Why is this important?
D.5.7.2(A) The (Pearson) chi-square is statistically significant (p = .056). This means that the relationship between two categorical variables (gender and geometry in hs.) is not statistically significant. Therefore, we cannot be confident that males and females are different on whether or not they took geometry in high school.
D.5.7.2(B) A good rule of thumb is that no more than 20% of the cells should have frequencies less than 5 which is stated in the footnote.
D.5.7.3 in output D.5.7.2: (a) how is the risk ratio calculated? What does it tell you? (b) how is the odds ratio calculated and what does that tell you? (c) how could information about the odds ratio be useful to people wanting to know the practical importance of research results? (d) what are some of the limitations of the odds ratio as an effect size measure?
D.5.7.3(A) The risk ratio is calculated by taking ratio of the students who did not take Algebra and they also had low math grades and divided by the students who did take Algebra 2. The risk ratio is often used to present the outcome of various groups (Wang, 2023).
D.5.7.3 (B) The odds ratio includes the risk ratios of the students with low and high math grades, and this tells you that one I almost three times as likely to get lower grades and high grades. The odds ratio is calculated by dividing the risk ratio for not taking algebra 2 with a lower math grade divided by the risk ratio for not taking algebra 2 with a higher math grade. This ratio combines both risks to compare the two. In this case, those that earned lower grades are 2.77 times less likely to take algebra 2 than those with higher grades.
D.5.7.3 (C). The odds ratio shows the probability of an event happening versus its compliment. Odds are binary in that the situation is an either/or. Showing the percentages of the likelihood a scenario will or will not happen is a useful tool in a study.
D.5.7.3 (D) Nothing provided within the data allows you to make a clear decision of what is a large odd.
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 D.5.7.3 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?
D.5.7.4(A) The most appropriate method of measurement would be Kendall’s Tau-b, highly educated fathers married highly educated mothers.
D.5.7.4(B) Cramer’s V is utilized for data that are measured at a nominal level but to measure the strength and the association between variables you would use Kendall’s tau-b. Kendall’s tau-b helps the end user to understand the random variables along with their order statistics (Fuchs,2021).
D.5.7.5 In Output 7.4: (a) How do you know which is the appropriate value of eta? (b) Do you think it is high or low? Why? (c) How would you describe the results?
D.5.7.5(A) The appropriate value of eta is .328 because in SPSS the eta will always be positive and because the dependent variable is math courses taken.
D.5.7.5 (B) This is medium to large value. This is because the measure of association is on a range of zero to one, with zero indicating no association whatsoever and one indicating a high association. An eta of .24 is medium to typical, while an eta of .37 is larger than typical.
D.5.7.5 (C) Research was conducted to examine the association between the number of math courses taken and academic track. The results were measured using eta, generating a value of .33. This indicates a medium to large strength of relationship between students who are on the fast track and students who take multiple math courses.
References
Fuchs, S., & Schmidt, K. D. (2021). On order statistics and Kendall’s tau. Statistics & Probability Letters, 169, 10-22.
Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for Introductory Statistics: Use and Interpretation: Use and Interpretation. Routledge.
Wang, W., Lu, S., & Xie, T. (2023). Optimal confidence intervals for the relative risk and odds ratio. Statistics in Medicine, 42(3), 281-296.
2. Robert
D.5.7.1 “Count” and “expected count”
The count would be the number of participants in a case, whereas the expected count is the number of participants you would expect to see according to the distribution if the variables were independent. For the fast track, 71 % of the kids in fast track have low math grades. However, the weighted area in this says the weighted average should be 58.7% instead of 71%. This would mean a researcher should only expect to see 19.9 students with Low math scores. Actual results show 4 more students than expected. The Chi-Square tells us if this difference is not due to chance (Morgan, Barrett, Leech, & Gloeckner, 2020).
D.5.7.2 (Pearson) chi-square
The chi-square tells a researcher if the relationship between the statistically significant, however, it does not tell how strong the relationship is between the variables. The chi-square requires a larger sample according to Morgan et al. (2020), one of the requirements for the Pearson chi-square is that expected values must be greater than 5 in 80% of the tables, and if the degrees of freedom is one then none of the cells should be less than 5 is so a Fisher Exact test should be used.
D.5.7.3 Risk ratio and Odds ratio
The risk ratio is the risk of the same event happening in one group as the second group. It is calculated by the occurrences in group 1 divided occurrence in the second group. The odds ratio is the risk ratio for the first group divided by the risk ratio of the second group (Morgan, Barrett, Leech, & Gloeckner, 2020). The Odds ratio is practical because it provides a measure of the strength of exposure and the outcome. This can be useful for decision-making as it measures the effect of the independent variable on the dependent variable.
D.5.7.4 phi, Cramer’s V, or Kendall’s tau-b
Since the output for 7.3 used nominal data, meaning there was no order or ranking to the information, a 3X3 crosstabulation was performed on the example. However, if the decision is to change the variable types to ordinal, then the researcher should use Kendall’s Tau-b. Cramer’s V requires nominal variables as does Phi (Morgan, Barrett, Leech, & Gloeckner, 2020).
In order to interpret the relationship between the two variables, researchers should conduct a Kendall’s Tau-b. This statistic shows a statistically significant association as the Kendall tau-b is .572, and p = <.001. This shows more highly educated parents married each other and less educated parents married each other. The main difference between Cramer’s V and Kendall tau-b is that the use of different variables for input. Kendall tau-b is used to measure the association of ordinal variables, while Cramer’s measures the strength of effect on two nominal variables (Morgan, Barrett, Leech, & Gloeckner, 2020). D.5.7.5 ETA Eta measures the association between nominal and normal/scale variables. The appropriate value for eta is the value based on the dependent variable. So in the example where math courses taken are the dependent variable, we would use the value .328 instead of the eta of the academic tract (Morgan, Barrett, Leech, & Gloeckner, 2020). Eta was used to determine the strength of the association between academic tract and math courses taken. Since eta requires the determination of the dependent variable, math courses taken are considered the dependent variable for this example. An eta of greater than .45 is considered much larger than typical, above .37 is larger than typical, and above .24 is considered moderate or typical. While the eta of .33 is below .37 it is still on the high side of typical. This shows there is a moderate to strong association between academic tract and the number of math courses taken. References Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for Introductory Statistics Use and Interpretation. New York, NY: Routledge. 3. Rita D5.7.1 In Output 7.1: (a) What do the terms “count” and “expected count” mean? (b) What does the difference between them tell you? D5.7. (a) The term “count” represents the number of students participating in the cell. Twenty-four students had low math grades in the fast track and 20 in the regular track. The expected count represents the expected number of students with low grades in the fast track, which was 19.9 and 24.1 in the regular track (Morgan et al., 2020). (b) The difference between them tells us that a higher percentage of students had low math grades in the fast track (Morgan et al., 2020). D5.7.2 In Output 7.1: (a) Is the (Pearson) chi-square statistically significant? Explain what it means. (b) Are the expected values in at least 80% of the cells > 5? How do you know? Why is this important?
D5.7.2 (a) The Pearson chi-square is not statistically significant (p = .056); according to Morgan et al. (2020), the indication says it cannot be specific fast track and regular track students are systematically different on whether they have low or high grades. (b) 0 cells have an expected count of less than 5, and the minimum expected count is 14.05 (Morgan et al., 2020). The phi is .22, and the maximum value should be less than 1.00 (Morgan et al., 2020). The symmetric measures table provides measures of the strength of the relationship of effect size. If the association between variables is weak, the statistics’ value is relatively close to zero (Morgan et al., 2020). This is important because the phi in this case, is a smaller sized effect than a typical in the behavioral science (Morgan et al., 2020).
D5.7.3. In Output 7.2: (a) How is the risk ratio calculated? What does it tell you? (b) How is the odds ratio calculated and what does it tell you? (c) How could information about the odds ratio be useful to people wanting to know the practical importance of research results? (d) What are some limitations of the odds ratio as an effect size measure?
D5.7.3. (a) The risk ratios are calculated when there are two dichotomous variables; thus, a 2×2 contingency table or cross-tabulation is used (Morgan et al., 2020). According to Morgan et al. (2020), these ratios are commonly used to report medical, applied health, and prevention science results. The first risk ratio is 1.53, computed by dividing 70% of students with low math grades who did not take Algebra 2 and 45.7% of students with low math grades who took Algebra 2 (Morgan et al., 2020). The second risk ratio is .553, computed by 30% with high math grades who did not take Algebra 2 divided by 54.3% with high math grades who did take it (Morgan et al., (2020). This indicates that the risk ratios are statistically significant (Morgan et al., 2020).
(b) The odds ratio is also calculated like the risk ratios when there are two dichotomous variables, and thus, it is a 2×2 contingency table or cross-tabulation (Morgan et al., 2020). The odds ratio of 2.77 is a ratio of ratios calculated at 1.531/.553 = 2.77 (Morgan et al., 2020). This tells us that the odds of failing to take Algebra 2 are 2.77 times higher for those with low math grades than those with high math grades (Morgan et al., 2020).
(c) Whether or not students took Algebra 2 and their math grades were high or low were binary variables; neither alternative was rare; an odds ratio was computed (Morgan et al., 2020). The odds ratio was 2.77, indicating that the odds of students failing to take Algebra 2 were 2.77 times higher if they had low math grades compared to if they had high math grades (Morgan et al., 2020). The 95% confidence interval was 1.07 to 7.15 (Morgan et al., 2020).
(d) Odds and risk ratios are typical examples of a third group or family of effect size measures, called risk potency measures (Morgan et al.,2020). When both variables are dichotomous, they are also called binary; especially in the health-related field, there are no agreed-upon standards for what represents a large ratio (Morgan et al., 2020). The ratio may approach the infinity of the outcome, which is rare or common, even when the association is new and random (Morgan et al., 2020).
D5.7.4 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?
D5.7.4 Kendall’s tau-b measures the strength of the association if both variables are ordinal; therefore, Kendall’s tau-b is appropriate because the variables are ordinal (Morgan et al., 2020). The p is < .001 for Kendall’s tau-b, which is significant, and the effect size tau-b = .572 is large, and the interpretation of tau-b is like that of r (Morgan et al., 2020). The main difference between tau-b and Cramer’s V is that tau-b has ordinal variables, and Cramer’s V has nominal variables (Morgan et al., 2020). D5.7.5 In Output 7.4: (a) How do you know which is the appropriate value of eta? (b) Do you think is high or low? Why? (c) How would you describe the results? D5.7.5 (a) The appropriate eta for this problem is .328 because they view math courses taken as dependent variables (Morgan et al., 2020). (b) According to Morgan et al. (2020), the eta is a medium to large effect size because, in the SPSS program, the eta ranges from zero to +1.00. (c) The eta was used to investigate the strength of the association between academic track and the number of math courses taken, and the result of the eta was .33 (Morgan et al., 2020). This eta is a medium to large effect size with 75 subjects and would probably be statistically significant (Morgan et al., 2020). References: Morgan, G.A., Barrett, K.C., Leech, N.L., & Gloeckner, G.W. (2020). IBM SPSS for Introductory Statistics: Use and Interpretation (6th ed). Routledge 4. Laura Discussion Thread: Chi-Square, Cross Tabulation, and Non-parametric Association Chapter 7 Interpretation Questions D.5.7.1 In Output 7.1: (a) What do the terms “count” and “expected count” mean? The terms “count” and “expected count” describe respectively the number of subjects we count based on our sample and the number of subjects we should expect to count if the Null Hypothesis is valid, or if there is no significant difference between my results - from my sample - and the count in the actual population. In this specific output, 24 males and 20 females received failing grades. The “expected count” is the number of males (or females) that we expect to see if there is no correlation between the variables we chose to analyze. It’s important to specify that we are trying to establish if there are correlations between our variables and also if these correlations are significative or if they are just the result of chance by choosing our sample (that is clearly not perfectly representative of the actual population) (Morgan at al., 2020). D5.7.1. In Output 7.1: (b) What does the difference between them tell you? The difference between the “count” and the ‘expected count” tells if the perceived correlation between males and females in relation to the grades they received is a real pattern or if it is only based on a casual discrepancy that the sample may not be perfectly representative of the actual population. So really does a pattern tell us that gender plays a role in the grades students receive or it is just something happening by chance in the sample we have chosen? The bias could be given for example, by the fact that the sample was not large enough. When the sample is large enough we observe that the patterns present in the sample tend to approach the patterns existing in the actual population. But since we cannot afford to get such a large sample we investigate the presence of such patterns being real or just perceived by using different statistical tests. D.5.7.2 In Output 7.1: (a) Is the (Pearson) chi-square statistically significant? Explain what it means. The Chi-Square is used to find patterns between nominal variables like dichotomous variables. Calculating the mean wouldn’t make much sense for these variables and so we can talk about proportion. Like for example 55% of females have good grades etc. Regression is used to represent patterns existing between numeral/interval/ratio variables while for nominal variables we use tables. Chi-square is a test that represents the degree - from strong to weak - that these patterns between nominal variables have. Then the pattern will be compared with the Null Hypotheses in order to determine if it is representative; if it is, the Null Hypothesis will be rejected (Spanos, 2019). In this case, the Pearson chi-square suggests that there are no significative patterns in our measurement. D5.7.2. In Output 7.1: (b) Are the expected values in at least 80% of the cells ≥ 5? How do you know? Why is this important? In order to perform a Chi-Square test that gives us significant results there are some premises we need to follow. For example, the Chi-Square test makes sense if expected values of at least 5 are counted in 80% of the cells. The difference between the expected values and the observed counts is in any case less than 5, which means that the expected values are in at least 80% of the cell. This is an important premise for running the Chi-Square test to verify if the correlation we found in the observed data is real or just the result of chance in sampling. D.5.7.3 in output D.5.7.2: (a) how is the risk ratio calculated? What does it tell you? The risk ratio is the ratio between the percentage of the students who have not taken Algebra 2 in high school and the students who instead have taken it. The students who did not take Algebra 2 in high school are 1.531 times more likely to perform poorly in Math. D5.7.3. in output D.5.7.2: (b) how is the odd ratio calculated and what does that tell you? The odd ratio is calculated by dividing the number representing the probability of failing Algebra 2 because of poor grades (1.531%) by the ratio indicating students who did well in Arithmetic but did not take Algebra 2 (0.553%). The odd ratio 1.531/0.553 is a favorable one and indicates the increased probability of performing poorly in Math when not having taken Algebra 2 (Morgan et al., 2020). D5.7.3. in output D.5.7.2: (c) how could information about the odds ratio be useful to people wanting to know the practical importance of research results? The odds ratio is used in particular in the medical field to compare two groups and to show the probability that the members of one group are also represented in another group. For example, using a cross table of people depressed and people taking a certain medication the odd ratio (expressed as a percentage for more clarity) indicates the probability of being depressed while taking a certain medication or of being depressed while not taking such medication. It is the case of being extra careful in drawing conclusions and remembering the old saying: “Correlation doesn’t necessarily mean causation”. It may be useful to know that in probability theory the odd is the opposite of the probability. So if the probability of launching a die and getting three is 1/6, the probability of not getting three is 5/6 and the odd is 1/5. This is helpful in understanding that the odd ratio represents the probability of an event manifesting after a specific variable to the probability has been missing. This ratio is used in Statistics because it carries some mathematical interesting advantages in furthering more calculations. D5.7.3. in output D.5.7.2: (d) what are some of the limitations of the odds ratio as an effect size measure? This index can be used only with dichotomous variables. The odd ratio needs to be used carefully because it may overestimate a situation. When the odd ratio represents a collateral risk, it may grow exponentially more and more and the primary risk grows as well (Morgan et al., 2020). In some cases, it may be not very easy to understand and interpret. 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 D.5.7.3 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? When dealing with nominal variables and using a Chi-square test, the Phi measures how strong is the correlation between such variables. If we watch output 7.3 on the father’s and mother’s level of education we can observe that Phi is not appropriate for a three-by-three table, as indicated in the picture. In fact, it is better to use Cramer’s V test which measures how strong is the relationship between two nominal variables when they have more than two values. When both variables are ordinal is better to use Kendall’s tau-b test. The correlation between the father’s and mother’s education calculated using the Kendall test gives a value of 0.572 and the p is less than 0.001. In conclusion, fathers tend to be married with mothers having a similar level of education (Morgan et al., 2020). D.5.7.5 In Output 7.4: (a) How do you know which is the appropriate value of eta? The ETA test is another measurement of the correlation between two variables. This correlation is measured on a range from zero to one, from very weak to very strong. Watching outcome 7.4 regarding the Math-courses-taken table the ETA measures 0.328. It is observed that males are just barely more likely to take more Math courses than females. D5.7.5. In Output 7.4: (b) Do you think it is high or low? Why? It seems to be moderate considering that runs on a scale between zero and one and it is slightly under one-half. I think it is moderately low because gender it’s only 0.11% of the shared common variance between the two variables (Morgan et al., 2020). D5.7.5. In Output 7.4: (c) How would you describe the results? Seems that students on the fast academic track tend to take more Math courses with respect to the other students, as well as males tend to take more Math courses than females. References Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for Introductory Statistics Use and Interpretation (6th ed.). New York, NY, USA: Routledge. Spanos, A. (2019). Probability theory and statistical inference: Empirical modeling observational data (2nd Ed.). Cambridge University Press.

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