Solved by verified expert:In Unit 6, you developed three different research questions that could be addressed using a one-sample, dependent samples, or independent samples t-test. In Unit 7, you expanded the research question that should be addressed using the independent samples t-test, to include more than two groups. In this unit you will further expand your One-Way ANOVA question to include two independentvariables.Two-Way (factorial) ANOVA: Expand your research question from Unit 7 to include a second independent variable with at least two groups (levels). Write out your new expanded research question. List and describe both of your independent variables and the levels or groupings within each independent variable. Also note your dependent variable. Define your Choices: Why you have chosen to investigate these two independent variables? How do you think they will affect your dependent variable? Testing and Predicted Results: What type of interaction do you expect to see between your independent variables? How might this interaction affect the dependent variable? Predict Results: Predict and share your hypothetical results and conclusions for all of your groups and interactions. Write a paragraph describing the final conclusion of your research assuming that you reject all of the null hypotheses (Ho1, Ho2, and Ho3). Be sure to talk about what the Post Hoc test might show in this case and the possible interactions between your two independent variables with respect to your dependent variable. While you are welcome to use SPSS, it is not required for this Discussion.

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Running head: ANOVA TESTS FOR COMPARING MULTIPLE SAMPLE MEANS

ANOVA Tests for Comparing Multiple Sample Means

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Course

Date

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ANOVA TESTS FOR COMPARING MULTIPLE SAMPLE MEANS

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ANOVA Tests for Comparing Multiple Sample Means

I am describing the use of a two-sample independence test to assess the differences or

similarities existing the scores registered by students of public and private schools. The goal of

this test is to determine whether the students of a private school are higher than the scores of a

public school. This test is however limited in the sense that it considered only one school of each

type, as the independence sample t-test is defined by the comparison of a maximum of two

samples. While the analyst could potentially conduct a series of different hypothesis

independence tests, the realization of such a high number of tests would have been extremely

tedious work. Worst even, the fact that the analyst could compare exclusively two samples at a

time would leave the pave open to doubts as to whether he had examined the appropriate schools

to address the research question (Gravetter & Walnau, 2016).

As opposed to a scenario of performing multiple t-tests, the analyst could have employed

a one-factor ANOVA test for the comparison of various sample means. The advantage of using a

one-way ANOVA test is that it enables the analyst to compare the means of all the schools

immediately. It will also allow the evaluation of whether the mean score of the students was the

same in all the schools or if there is at least one school in which the students scored a higher or

lower mean than in the rest of schools (Mertler & Reinhardt, 2016). While having more ready

access to this information, the ANOVA test per se is unable to predict which is the school

showing such a different mean score compared to the rest of schools. If the one-way ANOVA test

indicates that there is at least a sample separate from the rest, the analyst would then need to

perform a post-hoc analysis to identify which is the different sample.

From the above, the research question applicable to the current analysis would be of the

type “Does the school have any influence on the mean score of students on a standardized test?”.

ANOVA TESTS FOR COMPARING MULTIPLE SAMPLE MEANS

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As discussed previously, a one-way ANOVA test would be the best approach to evaluate this

research question, as it enables the simultaneous comparison of the mean score of students in

multiple schools. If necessary, the analyst can then complement this test with a post-hoc study to

identify which schools show a different performance to the rest.

The hypotheses tested through this one-way ANOVA test are:

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Null hypothesis: The school does not affect the mean score of its students in the

standardized test, as all the mean values reported by the different schools are

equivalent to each other. This hypothesis could be written as µ1 = µ2 = µ3 = … = µn,

where the sub-index represents each of the different schools included in the survey.

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Alternative hypothesis: The school has some effect on the mean score of its students

in the standardized test since at least one of the schools shows a different mean from

the rest. This hypothesis could be written as µ1 ≠ µ2 ≠ µ3 ≠ … ≠ µn.

One critical aspect of accounting for in the realization of this survey is that all the

students in the different schools need to perform the same type of test. This aspect is essential

because failing to do so may introduce additional sources of variability in the results, which

would potentially confound the obtained conclusion from the analysis. The data collected for the

study will thus involve the scores obtained from the different students in each of the schools. The

number of schools or samples included in the analysis would, in principle, be as high as possible.

A total of 20 schools seems to be a logical approach as a compromise between having a high

number of schools and maintaining a low cost for the analysis. In this sense, if the students of so

many schools have similar scores resulting in the absence of enough evidence to support the

rejection of the null hypothesis it is unlikely that including more schools will vary the obtained

result. Ideally, these 20 schools will comprise both public and private schools.

ANOVA TESTS FOR COMPARING MULTIPLE SAMPLE MEANS

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The sample size or the number of students in each of the schools that takes part in the

survey, on the other hand, would be of 30 to obtain a detailed evaluation of the mean score

recorded by the students in each of the different schools. Consequently, the full survey will

comprise a total of 20*30 = 600 data.

The scores obtained for the different students in the 20 schools will not likely differ

substantially, as the variability in the student performance within the various schools is likely to

be of the same order of magnitude than the variability between the different schools (Bernacki,

Nokes-Malach, & Aleven, 2015). Consequently, the one-way ANOVA test will most likely result

in a low F score and a high p-value, above the .05 target significance level, that indicates that

there is not enough evidence to support the rejection of the null hypothesis. If performed, the

post-hoc study will thus not show any substantial difference between the mean scores obtained

on the different schools.

ANOVA TESTS FOR COMPARING MULTIPLE SAMPLE MEANS

References

Bernacki, M. L., Nokes-Malach, T. J., & Aleven, V. (2015). Examining self-efficacy during

learning: variability and relations to behavior, performance, and learning. Metacognition

and Learning, 10(1), 99-117.

Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the behavioral sciences. Cengage

Learning.

Mertler, C. A., & Reinhart, R. V. (2016). Advanced and multivariate statistical methods:

Practical application and interpretation. Routledge.

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