Unit 7 Children with Disabilities - Two Way ANOVA Research question

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Mathematics

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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 independent variables.

  1. 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.
  2. Define your Choices: Why you have chosen to investigate these two independent variables? How do you think they will affect your dependent variable?
  3. 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?
  4. 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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1 Children with Disabilities – Unit 7 In this research, I want to compare the average of grades for 3rd-grade children with disabilities from Riverside Elementary School with the grades of 3rd-grade children without disabilities from three elementary schools in New Jersey (Riverside Elementary School, Roosevelt Elementary School and Lincoln Elementary School). The ANOVA test is appropriate for my research objective because I am comparing simultaneously more than two means. In this case, we will have to compare 4 groups at the same time. Do 3rd-grade children with disabilities from Riverside Elementary School have different grades than 3rd-grade children without disabilities from Riverside Elementary School, Roosevelt Elementary School and Lincoln Elementary School? Null Hypothesis (H0): There is no statistically significant difference in the average grades of 3rd-grade children with disabilities from Riverside Elementary School and 3rdgrade children without disabilities from Riverside Elementary School, Roosevelt Elementary School and Lincoln Elementary School. (µ1 = µ2 = µ3 = µ4). Alternative Hypothesis (H1): At least one of the grades average of 3rd graders from Riverside Elementary School, Roosevelt Elementary School and Lincoln Elementary School differs significantly. (µ1 ≠ µ2 ≠ µ3 ≠ µ4). The independent variable present in this study is the school grade of children from the above-mentioned schools, which in this scenario is the 3rd grade. The dependent variable is represented by the mean of grades that students in 3rd grade obtain. The levels of our dependent variable are represented on a scale from 1 to 10 (F to A+). For my research study, I will only use quantitative data of the scale type, because the ANOVA test can only compare the means of more than two groups, and the mean can 2 only be calculated for ratio and interval type variables, as a measure of central tendency. I want at least 20 observations for each of my selected groups, so there will be a minimum of 80 observations (sample size = 80). However, Riverside Elementary School has to have at least 20 children with disabilities in the 3rd grade, otherwise, I will search for another school. For the ANOVA test statistic, I will use a significance threshold of 0.05 (alpha value) and I expect to reject the null hypothesis, saying that at least one of the grades average of 3rd graders from Riverside Elementary School, Roosevelt Elementary School and Lincoln Elementary School differs significantly. In other words, with a 95% confidence, we can state that there is enough evidence to confirm that the grades of children with disabilities in the 3rd grade are statistically different from the grades of at least one of the other elementary schools. To test which pair differs significantly, I will apply a post hoc analysis using the Tukey-Kramer test and I expect to get the result that the mean of 3rd-grade children with disabilities is different from all the other three groups, while those do not have statistically significant differences between them. 3 References Aron, A., Coups, E., & Aron, E. (2013). Statistics for Psychology. Pearson.
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1
Children with Disabilities – Two Way ANOVA
For my project, I want to compare the average of grades for 3rd-grade boys and girls
with disabilities from Riverside Elementary School with the grades of 3 rd-grade boys and
girls without disabilities from three elementary schools in New Jersey (Riverside
Elementary School, Roosevelt Elementary School and Lincoln Elementary School). The
Two-Way ANOVA test is appropriate for my research objective because I am comparing
simultaneously more than two means, and the sample is defined in two ways by two
independent variables (disability and gender). The dependent variable is the 3rd-grade...


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