Bivariate descriptive statistics: introduction  (Page 2/3)

We are interested in whether there is a relationship between a person’s gender and how they typically get to school. In other words, is there a difference between men and women with respect to the type of transportation they use to get to school? To answer this question we must look at percentages, since the numbers of men and women are unequal.

Notice that the question about the difference in the relationship is stated in terms of whether or not the percentages are the same. To answer this question, you must first calculate the percentages for each box in the table so that you can make a comparison. However, there are three different types of percentages that you can calculate, and you need to choose the right type to make a meaningful comparison. You can calculate a percentage based on the Table Total for the entire table, or on the Column Totals , or on the Row Totals .

Start off by calculating the row totals, column total, and the overall total (or sample size). There are two rows, so there will be two row totals, one for the Females and one for the Males. For the females, there are 4 who ride a bike, 20 who use a car, and 45 who walk. The Row Total for females is, therefore, 4 + 20 + 45 = 69. Similarly, you should find that the row total for males is 61. Write the two row totals (69 and 61) into the boxes provided under ROW TOTAL.

There are three columns, so you will have three column totals. The column total for Bike is 17. Write that in for the Bike column total, and then calculate and fill in the column totals for Car and Walk.

The Table Total is just the sum of the counts in all six cells. So, you can either add up all of the cell counts, or you can add up just the two row totals, or you can add up just the three column totals. Any one of the three methods will give you exactly same value for the Table Total. In fact, it is a good idea to calculate the Table Total in at least two ways to make sure the two calculations agree.

Now that you have all of the totals, it’s time to decide which type to use to calculate the percentages for each cell. To do this, you need to consider the question that is asked: Is there a difference between men and women with respect to the type of transportation they use to get to school? The question focuses on the difference between men and women, so gender is our dominate variable. Since men and women are represented by the rows in the table, we want to use the ROW TOTALS to calculate ROW percentages.

Calculate the row percent for each cell. For example, there are 4 women who bike. The Row Total for women is 69. So the Row % for that cell (females who bike) is equal to 4/69 x 100 = 5.8%. And that is what you write after ROW % = in the first cell. As another example, there are 23 men who walk. The Row Total for men is 61. Therefore, the Row % for that cell (men who walk) is 23/61 x 100 = 37.7%. Use this same method to calculate the other four row percentages and write them into the table.