Data Interpretation & Analysis Flashcards

A researcher reports that a new teaching method improved test scores with a p-value of 0.03 and an effect size (Cohen's d) of 0.12. Which conclusion is most accurate?

Answer: The result is statistically significant but the practical effect is negligible

A p-value of 0.03 means the result is statistically significant (below the 0.05 threshold), but Cohen's d of 0.12 is considered a very small effect size (small ≥ 0.2, medium ≥ 0.5, large ≥ 0.8). With large enough sample sizes, trivially small differences become statistically significant. The practical (real-world) impact here is negligible despite the significant p-value.

The table below shows quarterly sales (in R thousands): Q1=120, Q2=144, Q3=138, Q4=165. A manager claims sales grew by 37.5% over the year. Which statement best evaluates this claim?

Answer: The claim is correct because (165−120)/120 × 100 = 37.5%

(165 − 120) / 120 × 100 = 45/120 × 100 = 37.5%. The calculation is mathematically correct. While Q3 did dip relative to Q2, the claim specifically compares Q1 to Q4 (start to end of year), which is a standard and valid way to report annual growth. The Q3 dip is relevant context but does not make the percentage claim incorrect.

A box-and-whisker plot shows: minimum = 14, Q1 = 22, median = 31, Q3 = 45, maximum = 78. A data point of 72 is reported. Which statement is correct?

Answer: 72 is not an outlier because it lies within the range of the data

The IQR = Q3 − Q1 = 45 − 22 = 23. The upper fence for outliers = Q3 + 1.5 × IQR = 45 + 34.5 = 79.5. Since 72 < 79.5, it does NOT qualify as an outlier by the standard 1.5×IQR rule. The maximum of 78 also exceeds 72, confirming 72 falls within the normal data range. Distance from the median is not a valid outlier criterion.

Two variables X and Y have a Pearson correlation coefficient of r = −0.87. A student concludes: 'X causes Y to decrease.' What is the most precise critique of this conclusion?

Answer: Correlation establishes direction but not causation; a third variable may explain the relationship

r = −0.87 indicates a strong negative linear relationship — as X increases, Y tends to decrease. However, correlation never establishes causation. A confounding variable (lurking variable) could be driving both X and Y, or the direction of causality could be reversed (Y causes X), or the relationship could be coincidental. The strength of r only tells us about the linear association, not the mechanism.

A pie chart shows market share: Company A = 35%, Company B = 28%, Company C = 22%, Company D = 15%. A bar graph of the same data shows Company A's bar appears twice as tall as Company C's. Which statement is correct?

Answer: The bar graph is misleading because a truncated y-axis is likely distorting the visual proportions

35% is only about 1.59 times 22%, not twice as large. If the bar for Company A appears twice as tall as Company C's bar, the y-axis almost certainly does not start at zero (truncated axis). This is a common graphical distortion that exaggerates differences between values. The pie chart data is internally consistent (35+28+22+15=100%), so the pie chart is not the problem — the bar graph's visual scale is misleading.

A dataset of 9 values has a mean of 50 and a median of 44. An analyst adds a 10th value of 44. Which outcome is certain?

Answer: The mean will decrease and the new median will equal 44

Adding 44 to the dataset: The new mean = (9×50 + 44)/10 = (450+44)/10 = 49.4, which is less than 50 — so the mean decreases. For the median: with 10 values, the median is the average of the 5th and 6th values when sorted. Since the original median was 44 (the 5th of 9 values), adding 44 means both the 5th and 6th values in the sorted 10-value set will be 44, making the new median exactly (44+44)/2 = 44. The median stays at 44 with certainty.