Past exam of the digital social research: statistics core course of the University of Oxford / 2019 / 2

All three frequency tables describe 2466 valid observations with no reported missing values. The sample is overwhelmingly White, Medium is the most common efficacy category, and disagreement with the technology-failure statement is more common than agreement. These statements describe the sample rather than establish population composition or causal relationships.

In a frequency table, a count gives the number of observations in a category, and a percentage divides that count by the full sample total. A valid percentage instead uses the total with an observed value of that variable. Here the two denominators coincide because every table reports zero missing values. A cumulative percentage adds categories in the displayed order; its substantive meaning depends on whether that order is meaningful.

The ethnicity counts are 77 Asian, 57 Black and 2332 White respondents, or 3.12%, 2.31% and 94.57%. Ethnicity is a nominal categorical variable: the displayed order is not a low-to-high ethnic scale. Its cumulative percentages are bookkeeping for that listing rather than an interpretable ranking. The two minority groups are small relative to the White group, which will matter for the precision and expected cell counts of the stratified comparisons.

For the three-category efficacy measure, 908 observations are High, 972 Medium and 586 Low, giving 36.82%, 39.42% and 23.76%. Medium is the mode, and 76.24% fall in the combined High-or-Medium categories. This is an ordinal categorical variable, but the table does not imply equal numerical distances between categories. Its order is descending efficacy, High then Medium then Low. Therefore the cumulative 76.24% refers to that upper portion of the scale, not to the proportion at or below Medium under an ascending convention. The cutpoints used to form these categories are not supplied and need not be invented to interpret their frequencies.

For techfail_chr, 336 strongly disagree, 922 disagree, 490 are neutral and 718 agree: 13.63%, 37.39%, 19.87% and 29.12%. The wording concerns not trusting technology because it fails when needed. Thus moving toward Agree means more distrust, not more trust. Combining the two disagreement categories gives $1258/2466\approx 51.01\%$, versus 29.12% agreement and 19.87% neutrality. Adding the separately rounded displayed percentages gives 51.02%; the difference is ordinary rounding error. There is no displayed strongly-agree category, so its frequency cannot be inferred or added to the agreement count.

The technology percentages add to 100.01%, including the printed valid-total figure. The integer counts still sum exactly to 2466; rounded percentages need not sum exactly to 100%. Finally, three separate univariate frequency tables say nothing by themselves about which efficacy categories the trusting or distrusting respondents occupy. That requires the joint information in the later contingency tables.