Past exam of the digital social research: statistics core course of the University of Oxford / 2021 / 2 / Solution

Each frequency table describes a marginal distribution, rather than a relationship among variables. The recorded two-category gender variable has 1,042 male and 1,093 female responses: 48.81% and 51.19%. It is a nominal categorical variable. Its ordering in the table supplies no quantitative ranking; a cumulative percentage over those arbitrarily ordered labels has no invariant substantive meaning.

Household income is an ordinal categorical variable with six bands. Their shares, from the lowest band upward, are $5.48\%$, $9.93\%$, $11.48\%$, $13.02\%$, $8.34\%$ and $51.76\%$. The highest band alone contains 1,105 respondents, slightly more than half the sample. The bands are not a numerical income measurement with equal steps: the top band is open-ended, so an exact sample mean income cannot be recovered from these category counts alone.

The agreement item is also an ordinal categorical variable. Combining the first two categories givesNeutral responses account for $447/2135\approx 20.94\%$; the two disagreement categories together account for $570/2135\approx 26.70\%$. These percentages describe the measured vaccination intention item, rather than actual vaccination status.

All three tables have 2,135 valid observations and no missing values for these variables, so their percentages and valid percentages coincide. This is different from the seven missing group-indicator values in question 1. The income and agreement columns sum to $100.01\%$ because the displayed percentages were rounded separately. That rounding is compatible with counts summing exactly to 2,135.

The tables alone cannot show whether the gender composition differs by income, or whether vaccination intention differs between groups. Those are questions about a joint contingency table and its conditional probabilities, not about separate marginal distributions.