Analyzing favorite cola preferences in a two-way table

Key concept: The two-way table for Pepsi, Coke, and Other shows how preference counts are distributed across male and female participants.

Step by step

Read the table structure carefully

The data are arranged as a contingency table with cola choice as the row variable and gender as the column variable. The row totals are 102 for Pepsi, 115 for Coke, and 56 for Other, while the column totals are 130 male, 143 female, and 273 total participants.

Because the study is a blind taste test, the main question is usually about whether preference appears to depend on gender or whether the choices are roughly similar across the two groups. Before making any conclusion, it helps to compare both within-gender and within-cola percentages rather than only looking at raw counts.

Compute the most useful percentages

For males, the proportions are:

• Pepsi: $50/130 \approx 0.385$
• Coke: $45/130 \approx 0.346$
• Other: $35/130 \approx 0.269$

For females, the proportions are:

• Pepsi: $52/143 \approx 0.364$
• Coke: $70/143 \approx 0.490$
• Other: $21/143 \approx 0.147$

These percentages show a noticeable difference: females selected Coke more often than males, while males chose Other more often than females. If the task asks for a comparison or interpretation, that pattern is the key result.

Interpret the association in the table

The table suggests an association between gender and cola preference because the conditional distributions are not the same. In a blind study, this kind of comparison is often used to check whether one subgroup favors a drink more strongly than another.

The overall favorite cola in the sample is Coke, with 115 votes out of 273. That is about

$115/273 \approx 0.421.$

Pepsi is next with 102 votes, and Other is last with 56 votes.

Common mistake with two-way tables

Raw totals alone can be misleading. Seeing 70 female Coke votes and 45 male Coke votes does not automatically prove women prefer Coke more, because there are also more female participants than male participants. The correct comparison uses conditional percentages, not just counts. Another common mistake is flipping rows and columns when computing proportions, which can produce a false pattern. Always identify whether you are comparing “within gender” or “within cola” before calculating.

A concise conclusion

The data show that Coke received the highest overall number of preferences, and the gender breakdown suggests that females favored Coke more strongly than males. The most informative statistical tool here is the two-way table with conditional percentages, not the raw counts alone.

Pitfall alert

A frequent mistake with this table is to compare 70 female Coke votes with 45 male Coke votes and stop there. That comparison ignores the different group sizes: there are 143 females and 130 males, so the raw counts are not directly comparable. Another issue appears when students compute percentages using the wrong total, such as dividing 70 by 273 instead of by 143. That changes the meaning completely. In a contingency table, always decide whether you are finding a row percentage, a column percentage, or an overall percentage before calculating. If that choice is wrong, the interpretation of preference can be misleading even when the arithmetic looks correct.

Try different conditions

If the table were changed so that the female Coke count was 60 instead of 70, the new table would still be a two-way contingency table with the same row totals adjusted accordingly. A possible variant question is: “Suppose the female Coke count is 60 and the other counts stay the same. Does Coke still appear to be the most preferred drink overall, and how does the gender pattern change?” In that version, you would recompute the row totals, the column totals, and the conditional percentages for each gender. This variant is useful because it checks whether you understand how a single cell in a table affects both the marginal totals and the association pattern.

Further reading

contingency table analysis, conditional percentages, association between variables