Comparing Several Means - Practice Lab

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California Baptist University *

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Feb 20, 2024

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Comparing Several Means (ANOVA) Practice Lab Background In a previous study, we found that high school students who spoke Korean as a first language scored higher on standardized English tests than students who spoke English or Spanish as a first language. This was surprising because they had less experience and familiarity with the language than the native English speakers. One possible explanation for this surprising finding is that the Korean students’ parents are highly involved in their education, keeping them accountable for their assignments and pushing them to achieve academically. In this practice lab, we will follow up on the previous study in order to better understand how these students’ experiences at home might explain their academic achievement. For this practice lab, we will use authentic data collected from 1,187 students (52% female, 48% male) at a large high school in the Los Angeles area. Among the students in the sample, 270 speak English as a first language, 859 speak Spanish as a first language, and 58 speak Korean as a first language. Parental involvement was measured using four survey items (e.g., “My parents support my learning at home”) with response options ranging from 1 ( Strongly disagree ) to 4 ( Strongly agree ). Standardized ( M = 0.0, SD = 1.0) composite scores are approximately normally distributed, ranging from -3.48 to 1.47. In this lab, we will determine whether primary language predicts parental academic involvement. To complete this lab, download and open the file called Family_Involvement.sav within SPSS. Analytic Method First, we must determine which statistical test is most appropriate for these data. Be sure to consider the levels of measurement of the independent and dependent variables. 1. Which statistical test is most appropriate for analyzing these data? A one-way ANOVA is the appropriate test for this data. 2. Why is this statistical test appropriate? A one-way ANOVA is appropriate because the independent variable (Primary language) is a nominal-level variable with three groups (English, Spanish< and Korean), and the dependent variable (family involvement) is a scale-level variable. There is only one independent variable. Hypotheses Next, we must state our null and alternative hypotheses both informally and formally. 3. What is the informal null hypothesis?

There is no significant difference in family involvement between the English, Spanish, and Korean primary language groups. 4. What is the formal null hypothesis? H 0 : µ ??𝑔𝑙𝑖?ℎ = µ ??𝑎?𝑖?ℎ = µ 𝐾???𝑎? 5. What is the informal alternate hypothesis? The levels of family involvement of the English, Spanish, and Korean primary language groups are not all equal. 6. What is the formal alternate hypothesis? H a : The means are not all equal Testing Assumptions The next step in our analysis is to generate descriptive statistics and graphs to help us inspect our data to see if they meet the assumptions of this statistical test. 7. What are the assumptions of this statistical test? The assumptions of the one-way ANOVA are normality, absence of outliers, and homogeneity of variance. Normality. We need to determine whether the distribution of family involvement scores within each group is approximately normally distributed. We will first generate a descriptive statistics table broken down by primary language. To do this, click Analyze ± Compare Means ± Means to open up the Means dialogue box. Select “Parent Involvement” from the variables list and move it to the Dependent List box on the upper right. Then select “Primary Language” and move it to the Independent List box on the lower right. Then click Options . Select “Kurtosis” and “Skewness” from the Statistics window and move them into the Cell Statistics box on the right. Click Continue . Then click OK . This should produce two tables in the Output Window. Copy and paste the “Report” table below:

8. Examine the skewness and kurtosis statistics for each of the three groups. Is the assumption of normality supported? All of the skewness and the kurtosis statistics have an absolute value of less than 1.0. They are all within the +/- 1.00 cutoff criterion. Therefore, we can conclude that the data are approximately normally distributed within each group. The assumption of normality is supported. Absence of Outliers. Second, we need to examine a boxplot to see if there are any outliers that could influence our results. To do this, Click Graphs ± Chart Builder . Next, click on Boxplot under the Gallery tab on the bottom left. Drag the first image in the gallery to the Drop zone on the top right. Select the independent variable from the variable list and drag it to the x -axis in the Drop zone. Next, select the dependent variable from the variable list and drag it to the y -axis in the Drop zone. Click OK . This should produce a graph in the Output Window. Copy and paste the bar graph below: 9. Examine the distribution of each language group. Based on visual inspection of the boxplot, are there any potential outliers? There are no apparent outliers (unusual observations) indicated on the boxplot.Thus, the assumption of absence of outliers is also supported.

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