![]() Then the percentage of the 21 respondents with no degree is: For example, only one of ours original 21 respondents had no degree. The percentages in Table 2.2 below have all been calculated using the steps described above: 1) obtain proportion, and 2) multiply by a 100. Since we established that reported actual numbers are meaningless for comparison purposes and that we need relative frequencies to do that, it would only make sense to add a relative frequency column to our educational attainment Table 2.1 from Example 2.2 (B). Relative frequencies are all nice and good, but let’s go back to our main quest, the frequency table. Since this type of fractions, depending on the context, can lead to an awkward phrasing (like in this case), you may choose to report a ratio in the way most apt for easier interpretation. This still tells us that men outnumber women as for every 1 man there is only a “0.7 woman”. It’s easy to see that if we want the women-to-men ratio, we only need to switch the numerator and denominator of the ratio: Using the numbers from the Watch Out!! #3 above, we can say that in the group of 170 respondents (102 men and 68 women), we have a men-to-women ratio of 1.5 - or, men in the study outnumber women by 1.5 to 1 since Also note that differences in percentages are expressed in percentage points, not in percent: in the current example, the difference between men and women who eat vegan is (19.1% – 16.7%=) 2.4 percentage points in favour of women being vegan, not 2.4 percent.Ī final way to express relative frequencies are ratios, where a ratio is simply one frequency/count relative to another: Note that while proportions range from 0 to 1 and typically get rounded up to three digits after the decimal point (e.g., 0.167 and 0.191), percentages range from 0 to 100 and usually get rounded up to one or two digits after the decimal point (e.g., 16.7% and 19.1%). That is, we could rephrase our finding and say that since only 16.7 percent of men reported being vegan while 19.1 percent of women did, clearly women are more likely to be vegan based on this particular group of respondents. Thus, we get the following percentages when comparing vegan men and women from the Watch Out!! #3 above: To convert proportions to percentages you only need to multiply by a 100 : In everyday life, people usually tend to use percentages to express that. In the example I used in the Watch Out!! #3 above, we concluded that more women than men were vegan based on the fact that the proportion of vegan women (0.191) was higher than the proportion of vegan men (0.167). You probably are more familiar with another way of expressing relative frequency - percentages. While actual numbers represent frequency, proportions are one way of expressing relative frequency. To make comparison possible - and meaningful - you should always use proportions or percentages (i.e., the numbers relative to the size of each group).Ī bit more notation then: if we denote frequency by f, and you recall that N stands for number (of elements in a dataset of people in a group, etc.), it would be easy to see that proportion - denoted by p - should be To conclude, never use numbers as counted to compare between groups (unless they are of equal size). Rather, it’s the other way around: more women than men tend to eat vegan, because vegan women are a higher proportion (i.e., the number for women is higher relative to their group size). That is, the proportion of vegan men (0.167) is smaller than the proportion of vegan women (0.191), so no, we cannot say that men tend to be vegan more than women do. What we should be asking ourselves instead is whether a larger proportion of men eat vegan, compared to women - and the correct answer would require a comparison of the numbers relative to group size.Ī quick calculation reveals that 17 out of 102 is actually less than 13 out of 68: Thus, maybe we find more vegan men than women simply because there are more men than women in the study. Yes, more men report eating vegan but men in the study outnumber women by 24 to start with. That is, comparison of the numbers as counted in the two groups has little meaning since it does not take into account group size. We cannot compare the two groups (men and women) directly since the groups have different sizes. If you go by the actual, counted numbers reported, you may decide that yes, the researchers’ conclusion is correct as 17 is more than 13, i.e., four more men than women have reported eating vegan. Can the researchers conclude that men tend to favour vegan diets more than women do? Say that the researchers found that 17 of the men and 13 of women reported a vegan diet. Imagine that researchers are conducting a study on eating habits and they have interviewed 170 people 102 identified as men and 68 identified as women. ![]()
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