We say that there is an association when the frequency of a category influences another category from a different categorical variable.
See solution.
Practice makes perfect
We say that there is an association when the frequency of a category influences the frequency of another category from a different categorical variable. To check this, we can compare the conditional relative frequency of a category with the corresponding marginal frequency. Let's consider the following two-way frequency table.
Hobbies
Gender
Reading
Video games
Movies
Total
Girl
12
10
18
40
Boy
16
26
18
60
Total
28
36
36
100
The table above shows the preferred hobbies from a group of boys and girls. From it, we can check if there is an association with gender and preferred hobbies. For this, we need to find the percentage of girls and boys interviewed.
&Percentage of girls &&Percentage of boys
& 60/100=0.60=60 % && 40/100=0.40=40 %
Now, if we wanted to check for a possible association — let's say, for girls and a preference in the hobbies listed — we need to find the corresponding conditional relative frequencies.
Of the 28 persons preferring reading, 16 are girls.
Of the 36 persons preferring video games, 26 are girls.
Of the 36 persons preferring movies, 18 are girls.
16/28= 0.571 = 57.1 %
26/36= 0.722 = 72.2 %
18/36= 0.5 = 50 %
Now, if there was no influence between the gender and the preferred hobbies, we would expect that the distribution of gender in each category to be roughly the equal to the distribution of gender within the whole group. Therefore, from the table above we can obtain the conclusions shown below.
Since 57.1 % is about the same as 60 %, the data suggest that girls are neither more or less likely to prefer reading.
Since 72.2 % is considerably greater than 60 %, the data suggest that girls are more likely to prefer video games.
Since 50 % is considerably less than 60 %, the data suggest that girls are less likely to prefer watching movies.
