Lilly collects data on a sample of 40 high school students to evaluate whether t

Question

Lilly collects data on a sample of 40 high school students to evaluate whether the proportion of female high school students who take advanced math courses in high school varies depending upon whether they have been raised primarily by their father or by both their mother and their father. Two variables are found below in the data file: math (0 = no advanced math and 1 = some advanced math) and Parent (1= primarily father and 2 = father and mother). a) Conduct a crosstabs analysis to examine the proportion of female high school students who take advanced math courses is different for different levels of the parent variable. b) What percent female students took advanced math class c) What percent of female students did not take advanced math class when females were raised by just their father? d) What are the Chi-square results? What are the expected and the observed results that were found? Are they results of the Chi-Square significant? What do the results mean? e) What were your null and alternative hypotheses? Did the results lead you to reject or fail to reject the null and why?

Explanation / Answer

To run the crosstabs analysis: Click Analyze ? Descriptive Statistics ? Crosstabs Click “parent” and move it to the “Rows” box Click “math” and move it to the “Columns” box A box in the bottom left corner called “Display clustered bar charts” should be checked. Keep it this way. Click “Statistics” and check the box next to “Chi-square” and “Phi and Cramer’s V” Click Continue. Click “Cells” and check the box next to “Expected” (the “Observed” box should already be checked). Also, click “Row” and “Column” in the percentages box. Click Continue. Click OK. Let’s get an idea of what we’re looking at here. On the outermost edges, you see a row called total and a column called total. Each row/column has two cells. In the upper right most cell of data, you get totals for the “primarily father” variable. 30 females in the sample of 130 were raised primarily by their father. Below that cell, you get the totals for females in the sample who were raised by father and mother (count = 100 out of 130 females in the sample). Looking at the lower left most cell of data, you can identify the total number of females in the same who have taken no advanced math (count = 113 out of 130 females in the sample). The cell to the right tells you how many females in the sample have taken some advanced math (count = 17 out of 130 females in the sample). Let’s identify the percentage of female students who took some advanced math classes. Now let’s identify the percent of female students raised by their fathers only. Cells on the interior of the table are conditional percentages. In other words, they ask: given a specified level of one variable, what percentage of these individuals fall into the various levels of another variable? What we’re doing here is focusing on just one level of a variable (e.g., primarily father level of the parent variable), and looking to see what percentage of people within this level appear in the levels of the other variable (i.e., what percentage of students raised primarily by their father took some advanced math classes or no advanced classes). Now let’s identify the percentage of female students who, given that they were raised by their fathers, took no advanced math classes. What’s the ?2 value for this analysis? How many degrees of freedom are associated with this test? Remember that for ?2 df = (rows – 1)(columns – 1) Formally, we would state this as: ?2(1, N = 130) = 9.83, p < .05. Each of our variables had just two levels, resulting in a 1df test. What does that mean? It means that we do not need to run follow-up tests. What can we say about the strength of the relationship between taking advanced math courses and level of parenting? Let’s look at an effect size for this analysis. What does F = -.28 mean? Rules of thumb for F and Cramer’s V .10=small .30=medium .50=large So, this is a medium effect. Let’s look at a clustered bar chart showing the differences in the number of female students taking some advanced math classes for the different categories of parenting. Remember how we left the box for “Display clustered bar charts” checked? SPSS has already created a barchart for us in the Output file. Let’s point out a few things about this chart. First, notice that the observed frequencies (called counts) appear on the y-axis, percentages do not. Also, notice that the observed frequencies for “some advanced math” between the two groups (raised by father, raised by mother and father) are not all that different, 9 and 8 respectively. However, remember that chi square tests are testing for differences between observed vs. expected frequencies. Now let’s create a clustered bar chart that displays percentages on the y-axis. Click Graphs ? Bar ? Select “Clustered” and “Summaries for groups of cases” and click Define. Select “% of cases” in the Bars Represent box Move “math” to category axis box Move “parent to define clusters by” box Click OK. We’re most interested in comparing the percentages in these two bars. If we were going to create a chart to accompany our result section, we would probably want it to look similar to this one (as opposed to the one SPSS automatically generates) because it provides a simple visual display of the two categories we are most interested in: females who have taken some advanced math courses who were raised by either their fathers only, or by both their mother and father. So all in all, what can we say about these two variables? Let’s put our conclusions in APA format: A 2 X 2 contingency table analysis was conducted to assess the relationship between childcare responsibility (father only versus father and mother) and enrollment in advanced math courses (none versus one or more). These variables were significantly related, ?2(1, N = 130) = 9.83, p < .05, F = -.28. The percentage of females who took advanced math courses is significantly higher for females who were raised by only their fathers (30%) than for females raised by both their mother and father (8%).

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