you’ve seen how to use a Goodness of Fit Test, a Test for Independence and an An

Question

you’ve seen how to use a Goodness of Fit Test, a Test for Independence and an Analysis of Variance to answer research questions relevant to those statistical analysis procedures. Respond to the following to demonstrate your grasp of these
- Describe a scenario where a researcher could use a Goodness of Fit Test to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
- Describe a scenario where a researcher could use a Test for Independence to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
- Describe a scenario where a researcher could use an Analysis of Variance to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
- The Goodness of Fit Test and Test for Independence both use the same formula to calculate chi-square. Why? I.e., explain the logic of the test.
- ANOVA is based on an F-ratio that is calculated as the ratio of two variance estimates, the variance between groups and the variance within groups, but enables conclusions to be made about the means of the samples involved. What is the logic of that? I.e., explain the rationale that supports the use of variance estimates. you’ve seen how to use a Goodness of Fit Test, a Test for Independence and an Analysis of Variance to answer research questions relevant to those statistical analysis procedures. Respond to the following to demonstrate your grasp of these
- Describe a scenario where a researcher could use a Goodness of Fit Test to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
- Describe a scenario where a researcher could use a Test for Independence to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
- Describe a scenario where a researcher could use an Analysis of Variance to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
- The Goodness of Fit Test and Test for Independence both use the same formula to calculate chi-square. Why? I.e., explain the logic of the test.
- ANOVA is based on an F-ratio that is calculated as the ratio of two variance estimates, the variance between groups and the variance within groups, but enables conclusions to be made about the means of the samples involved. What is the logic of that? I.e., explain the rationale that supports the use of variance estimates.
- Describe a scenario where a researcher could use a Goodness of Fit Test to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
- Describe a scenario where a researcher could use a Test for Independence to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
- Describe a scenario where a researcher could use an Analysis of Variance to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
- The Goodness of Fit Test and Test for Independence both use the same formula to calculate chi-square. Why? I.e., explain the logic of the test.
- ANOVA is based on an F-ratio that is calculated as the ratio of two variance estimates, the variance between groups and the variance within groups, but enables conclusions to be made about the means of the samples involved. What is the logic of that? I.e., explain the rationale that supports the use of variance estimates.

Explanation / Answer

- Describe a scenario where a researcher could use a Goodness of Fit Test to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?

Suppose researcher want to check whether the distribution of the observed data or observations is same as the population distribution or not, then researcher could use a Goodness of Fit test. Let us see an example. Suppose there is a package of chocolates with six different colors and researchers wants to check whether the proportion of the chocolates with different colors is same or not. Researcher wants to check whether the package contain all six colors in an equal proportion or not. Here, the Chi square test for goodness of fit is appropriate because we want to check whether the population distribution is same as the observed distribution of the colors of the chocolates.

- Describe a scenario where a researcher could use a Test for Independence to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?

Suppose Researcher wants to check whether the gender of the person and the political party for which person vote is independent from each other or not, then researcher would use chi square test for independence of two categorical variables. This test is appropriate to use, because there are two categorical variables such as gender of the person and political party and researcher wants to check whether there is any relationship exists between these two variables or not.

- Describe a scenario where a researcher could use an Analysis of Variance to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?

Suppose researcher wants to check whether there is any significant difference in average treatment effect of the four different types of drugs. Then researcher would use the Analysis of Variance or ANOVA for checking this claim. The variable involved in this study is the effect of drug. The ANOVA test is appropriate to use in this scenario because we have to compare more than two groups. For this study, we consider four groups of people or patients who are given four different types of drugs for their medication.

- The Goodness of Fit Test and Test for Independence both use the same formula to calculate chi-square. Why? I.e., explain the logic of the test.

Actually, in the both test we want to check the significant difference in the observed frequencies and expected frequencies and that’s why we use the same formula for calculation of chi square test statistic. Logically, both tests are same. In the goodness of fit, we consider the parent distribution and then compare it with observed distribution, while in test for independence we check independence of two categorical variables. In both cases, we compare observed and expected frequencies.

- ANOVA is based on an F-ratio that is calculated as the ratio of two variance estimates, the variance between groups and the variance within groups, but enables conclusions to be made about the means of the samples involved. What is the logic of that? I.e., explain the rationale that supports the use of variance estimates.

Although F statistic is the ratio of variance between groups and variance within groups, the variances are measured from the mean or averages. As we know the variance is calculated by subtracting the average or mean value from the different values of variable. So, this logic helps us to explain the comparison of the sample means.

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