4.2.3.2.4 Correlation analysis, coefficients and levels of measurement Quiz: AQA Psychology, Unit 2

The 20 questions

1. A correlation coefficient can take values:

   • From 0 to 100, where higher values show stronger relationships between the variables
   • From -1 to +1, where the sign shows direction and the size shows strength
   • From -100 to 100 as a percentage, so each unit shows one per cent of the link
   • Only positive values, from 0 to 1, where the size alone shows the strength of the link

2. A coefficient of 0 indicates:

   • A perfect positive relationship in which every point lies on a rising straight line
   • A perfect negative relationship in which every point lies on a falling straight line
   • A causal link between the variables, shown by a strong positive pattern on the graph
   • No linear relationship between the two variables

3. Nominal data are:

   • Continuous data with a true zero point, such as reaction time in milliseconds
   • Ranked data with unequal intervals between the ranks, such as finishing positions
   • Categories with no inherent order or equal intervals between them
   • Measurements with equal intervals and no true zero, such as temperature in Celsius

4. Ordinal data are:

   • Measurements with equal intervals on a scale, such as scores on a test with marks
   • Ranked in order, but the intervals between ranks are not necessarily equal
   • Categories with no order at all, such as colours or types of pet kept at home
   • Continuous measurements with a true zero point, such as the weight of each person

5. Interval data are:

   • Categories that cannot be ordered, such as the names of people in a class
   • Measured on a scale with equal intervals but no true zero
   • Ranked data with unequal intervals between each position in the list
   • Data that are always nominal, so they can only be counted as frequencies

6. Which correlation test is used for ordinal data?

   • Sign test for pairs
   • Chi-squared test of association
   • Pearson's r coefficient
   • Spearman's rho

7. Which correlation test is most appropriate for interval data that are normally distributed?

   • Chi-squared
   • Pearson's r
   • Sign test
   • Spearman's rho

8. A scatter diagram shows points that fall steadily from top left to bottom right. What correlation is shown?

   • A zero correlation with no pattern, so the points are scattered at random
   • A strong negative correlation, for example r = -0.9
   • A strong positive correlation, for example r = 0.9 for the same pattern
   • An unrelated pattern with r = 0, which shows no link between the two variables

9. A researcher finds r = 0.12 between two variables in a large sample. How is this best described?

   • A perfect correlation that matches every point on the scatter
   • A strong positive correlation between the two variables measured
   • A strong negative correlation that links the two measures together
   • A very weak positive correlation

10. Which of the following is an inappropriate use of correlation?

    • Correlating ranks of two judges' attitudes, which are ordinal and can be ordered
    • Correlating scores from two continuous rating scales that were both used in the study
    • Correlating two interval measures of time spent studying and the test scores gained
    • Correlating gender with a colour preference, because both are nominal categories

11. Interpret r = -0.45 between hours of phone use and sleep quality.

    • No relationship, because the value is below 0.5 and so cannot indicate any link at all
    • A strong negative correlation proving that phone use causes poor sleep in every case
    • A moderate positive correlation between the two variables, so more use gives better sleep
    • A moderate negative correlation: more phone use tends to go with lower sleep quality

12. A researcher reports r = 0.6 between two variables. What proportion of the variance do they share?

    • 6%
    • 36%
    • 0.6%
    • 60%

13. A researcher finds a significant correlation of r = 0.2 in a large sample. Why might this be practically unimportant?

    • The correlation shows that all the variance in the data is explained by the two variables, leaving no room for other factors
    • The coefficient is negative and so cannot be significant, because statistical significance only ever applies to positive values of r
    • The coefficient is strong enough to prove causation, so the link between the two variables is certain and needs no further testing
    • The coefficient is weak, so the variables share very little variance even if the result is statistically significant

14. A correlation coefficient of 0 does not prove that no relationship exists. Why?

    • Because correlations cannot be calculated for small samples, so the value is not valid
    • The relationship may be non-linear, which Pearson's r does not detect
    • Because the coefficient cannot be negative, so a zero means only a weak positive link
    • Because all correlations are always positive, so a zero value is impossible to reach

15. Which list correctly orders the coefficients r = -0.7, r = 0.3, r = -0.1 and r = 0.5 from weakest to strongest?

    • -0.1, 0.3, 0.5, -0.7
    • -0.7, 0.5, 0.3, -0.1
    • 0.3, -0.1, 0.5, -0.7
    • 0.5, -0.7, -0.1, 0.3

16. An outlier in a data set can have what effect on Pearson's r?

    • It changes the level of measurement from interval to nominal, so the coefficient can no longer be used at all for the data
    • It can substantially change the coefficient, potentially inflating or reducing the apparent relationship
    • It always makes the coefficient exactly zero, which hides any relationship that really exists in the data set collected
    • It has no effect because Pearson's r ignores extreme values completely when the coefficient is calculated from the data set

17. Which statement about interval level of measurement is correct?

    • Interval data always have a true zero point, which means ratios can always be taken
    • Interval data have categories with no order, so the values cannot be compared at all
    • Interval data are always ranked, with unequal gaps between the positions on the scale
    • Equal intervals between values allow differences to be meaningfully compared

18. A researcher has ranked data from two judges and wants to know how closely their rankings agree. Which test is most suitable?

    • Spearman's rho
    • Mann-Whitney U
    • Pearson's r
    • Related t-test

19. Why might a researcher choose Spearman's rho over Pearson's r for a small data set with many tied ranks?

    • Spearman's rho works on ranks and does not assume interval data or a normal distribution
    • Spearman's rho always gives larger coefficients, so it makes any relationship look stronger
    • Spearman's rho requires nominal data, so it cannot be applied to ranks or numerical scores
    • Pearson's r cannot be calculated for any sample, because it needs ranks rather than values

20. A researcher finds r = -0.85 between practice hours and error rate. What is the best description?

    • A weak negative correlation with no practical meaning for the people who took part
    • A strong negative correlation: more practice goes with fewer errors
    • A strong positive correlation: more practice goes with more errors made during each session
    • A perfect correlation proving that practice reduces errors in every single person tested

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