Consult the diagram below for additional instruction on the process of hypothesis testing, Then, read through the summary and try the practice problems. If you would like more examples after trying these, follow the link to more sample tables at the bottom of the page.
To read a crosstabulation, follow these three steps: (1) determine if the result is statistically significant; if it is, then (2) interpret the pattern in the table; if not, stop; After you interpret the pattern (if the table is reliable), think about how the independent variable, in the columns, might be related to the dependent variable, in the rows.
You can picture the process like this:
Step 1.
Compare the value of "p" for Chi-square with the
conventional criterion, 0.05, or 5%.
If you are challenged by
decimal numbers, here is a simple technique for comparing values. Take
the value of "p" and mulitply by 1,000. To get the result, move the
decimal three places to the right, adding zeros if needed. For
example, if p = 0.014, we would end up with 14. If p = 0.11, we would
get 110. If p = 0.0057, we would get 5.7 . Next, do the same for the
criterion, 0.05. This will always result in 50. Finally, compare the
modified value of p with the modified criterion. For example, for p =
0.014, we have 14 compared to 50. Since 14 is less than 50, this
result would be reliable. For p = 0.11, we have 110 compared to
50. Since 110 is greater than 50, this result is not reliable. For p =
0.0057, we have 5.7 compared to 50. Since 5.7 is less than 50, this
result is reliable.
Step 2.
Compare the column percents across each row. If the
percents are consistently different, the independent variable is
related to the dependent variable.
Consider the following
table:
The percents across the
"Yes" row vary from 7.6 to 21. This suggests that members of some race
groups are more likely to belong to a labor union.
Step 3.
Interpret the results from a social scientific
perspective.
In the example from step two, we need to consider
some of the reasons why race might be related to labor union
membership. This will lead us to want to look for other variables. For
example, we might suggest that political view is involved. Labor
unions are considered a liberal institution, and some race groups tend
to be more liberal than others. Blacks tend to be more liberal than
whites, and therefore, are more likely to belong to a
union.
Another possibility is that some types of jobs are more
likely to be unionized than others, and some races are more likely to
hold those jobs. Service jobs are more likely to be unionzed than
clerical jobs, and blacks and asians are more likely to have these
jobs than whites.
Note that we are describing a relationship in
the aggregate, not the causal relationship for any particular
individuals. When we claim that blacks tend to be more liberal than
whites, we are not saying that all blacks are more liberal than all
whites, or that any particular black is more liberal than any
particular white. There are liberals, moderates and conservatives
among both race groups. The pattern describes general tendencies, or
probabilities, rather than particular cases.
Now, try to apply what you've learned with the following examples.
These data come
from the US Census, Current Population Study, 1998.
Answer the following questions about this crosstabulation. When you've finished, click on the "How did I do?" button. If you missed any item, go back, reconsider the question, and select a new answer. Then, click on the "How did I do?" button again. Keep working until you've correctly answered each question.
When you've correctly answered the questions for the first crosstabulation, try this one:
These data come
from the US Census, Current Population Study, 1998.
Would you like more practice with crosstabulations?