![]() ![]() Conditional Percents for Data in Table 6.2 Credit Card Response Figure 6.4 is an example of a cluster bar graph that displays the conditional percents for the data found in Table 6.3. Of course, the comparison of interest might also be displayed graphically in a cluster bar graph. However, since this doesn't usually happen, it is good practice to include the percentages most relevant to the problem at hand in the table and to include a total that allows the reader to quickly pick out what is adding to 100%. In this case, it was trivial to convert the counts into percents because the sample size is exactly 100 for each sample. Each of these percents is called conditional percents because each calculation is restricted to or contingent on the year in school. Table 6.3 shows the conversion of counts to percents for this sample. In this example, the most relevant percentages of interest for comparison are the ones that condition in the class rank. Conditioning on credit card ownership, we find that the percentage of credit card holders in the study who are seniors = 81 / 254 or about 32%. looking at the distribution within each column separately), we find that the percentage of Seniors who have a credit card is 81%. This is an example of a 2 × 4 contingency table because there are 2 rows and 4 columns to the data in the table. Responses to Credit Card Ownership by Year in School Credit Card Response The results for the responses to this question are found in Table 6.2 below. Question: Do you currently own at least one credit card? Numerical Summary of Hometown Description HometownĬonsider the following survey question that was asked of four different samples of Penn State students: 100 freshman (Fr), 100 sophomores (So), 100 juniors (Jr), and 100 seniors (Sr). Table 6.1 shows the distribution and the calculations for the data in Example 6.1. For one variable that just involves dividing the count in each category by the total to get the proportion - and then converting those to percents by multiplying the proportions by 100% (if percents are desired). Now, it is important to remember that before data is displayed in a bar graph like the one above, it must first be tabulated to calculate the percents that let us see the variable's distribution. The bar graph provides a more informative picture than a pie chart in this case as it allows us to see the natural ordering of the categories. We will address this sort of scenario in Section 7.4.0 10 14 53 25 8 20 30 40 50 60 Hometown Rural Suburb Small town Big city Pe r centįigure 6.2. The point estimate of the slope parameter, labeled b 1, is not zero, but we might wonder if this could just be due to chance. However, it is unclear whether there is statistically significant evidence that the slope parameter is different from zero. It is reasonable to try to fit a linear model to the data. The last plot shows very little upwards trend, and the residuals also show no obvious patterns. Instead, a more advanced technique should be used. We should not use a straight line to model these data. There is some curvature in the scatterplot, which is more obvious in the residual plot. The second data set shows a pattern in the residuals. The residuals appear to be scattered randomly around the dashed line that represents 0. In the first data set (first column), the residuals show no obvious patterns. ![]() \): Sample data with their best fitting lines (top row) and their corresponding residual plots (bottom row). ![]()
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