Outline of Today’s Discussion

1. Outline of Today’s Discussion • Practice in SPSS: Scatter Plots • Practice in SPSS: Correlations • Spearman’s Rho

2. Part 1 Practice in SPSS: Scatter Plots

3. Two Scales for Depression • HRSD • Hami Rating Scale for Depression • http://en.wikipedia.org/wiki/Hamilton_Rating_Scale_for_Depression • BDI • Beck Depression Inventory • http://en.wikipedia.org/wiki/Beck_Depression_Inventory • The “feelinggood.sav” sample file contains measures on both scales, and at two different times (Time 1 and Time 2).

4. SPSS: Scatter Plots & Headers • Please sign on to SPSS and load “feelinggood.sav”. • Let’s produce a scatter plot for now, focusing just on the pictorial information. Later we can get into numbers, i.e., correlations. • Let’s create a scatter plot in which we attempt to predict HRSD1(y-axis) given BDI1(x-axis). • We’ll use this path: Graphs--> Legacy Dialogs --> Scatter/Dot --> Simple Scatter Define --> (Assign X and Y) ---> OK.

5. SPSS: Scatter Plots & Headers • Would someone state a plausible r-value for this scatter plot? • Identify two implausible r-values for this scatter plot. • Now let’s try to again predict HRSD1 (y-axis), but the new predictor will be HRSD2 (same scale, at a later time) (x-axis). Add that scatter plot to the output. • In a moment we’ll see which variable (BDI1 or HRSD2) is the better predictor…

6. SPSS: Scatter Plots & Headers • Recall that the scientific method has 4 goals. Description Prediction Understanding (i.e., causal relations) Creating Change • Correlational stats (like the Pearson r) allow us to Predict!!! • The stronger the absolute value of ‘r’, the better the prediction…

7. Part 2 Practice in SPSS: Correlations

8. SPSS: Correlations Cars & GSS • Let’s compute the ‘r’ statistic relating HRSD1 (y-axis) to BDI1 (x-axis) . • To get the ‘r’ statistic, select Analyze correlate  bivariate  move x and y into “variables” box  select Pearson (for ‘scale’ measures).

9. SPSS: Correlations Cars & GSS • Now, let’s compute the ‘r’ statistic relating HRSD1 (y-axis) to HRSD2 (same scale, at a later time) (x-axis). • So, which variable (BDI1 or HRSD2) is the better predictor of HRSD1?

10. Part 3 Spearman’s Rho

11. Spearman’s Rho • Now, let’s load the GSS file and look at three other variables; Respondent Income, Highest Year of School Completed, and Age When First Married. • We’ll use a Spearman ‘r’ to predict Respondent Income, first from Highest Year of School Completed, then from Age When First Married. • So, which variable (Highest Year of School Completed or Age When First Married) is the better predictor of Respondent Income?

12. Spearman’s Rho Different correlational statistics are used for different measurement scales: Nominal Scales – The Phi statistic or Kendall’s Tau Ordinal Scales – Spearman’s r (a.k.a. Spearman’s rho) Interval or Ratio (‘Scale’) – Pearson’s r

13. Spearman’s Rho • This semester, we will not compute the Phi and Kendall-tau statistics (for nominal scales). • Later this semester, we will learn a statistic (chi-square) for evaluating associations among categorical (nominal) variables.

14. Spearman’s Rho • Like the Pearson correlation coefficient ( “r” ), the Spearman Rank Order Correlation(rho) indicates the strength of the relationship between two variables. • The Spearman, too, ranges from -1 to +1. • The difference is that, unlike the Pearson ( “r” ) which is used for interval or ratio scales, the Spearman is used for ordinal scales (ranks).

15. Spearman’s Rho Actually, there are three cases in which we should choose Spearman’s rho over Pearson’s r… • When both variables are on ordinal scales. • When one variable is ordinal, and the other is interval or ratio (“scale”). • When statistical assumptions underlying the Pearson ‘r’ are not met…

16. Spearman’s Rho Condition 1: When both variables are on ordinal scales…. Note: The Spearman formula is computationally simpler than the Pearson formula! d = rank differences n = pairs of scores Spearman’s rho = rs You will NOT have to memorize this formula.

17. Spearman’s Rho Condition 2: When One variable  Ordinal, and One variable  “Scale” (Interval / Ratio): The “Scale” variable needs to be converted to ranks. Then, Spearman’s rho is computed on the two sets of ranks. Note: Scores can be converted “downward in sophistication” –from “scale” to ordinal, or from ordinal to nominal. Scores can not be converted “upward in sophistication”!!! More on converting scores in a minute…

18. Spearman’s Rho Condition 3: When the assumptions for Pearson’s ‘r’ fail. Assumptions of Pearson’s ‘r’: 1. Scores on each variable are normally distributed. 2. The variances are approximately equal for the variables. 3. Each score is independent of any other score. We will return to the notion of assumptions later in the semester!

19. Spearman’s Rho • Let’s return to the issue of converting scores from an interval or ratio scale, to an ordinal scale. • Assume that we have 10 pairs of scores. • Assume also that we want to convert all scores to an ordinal scale, perhaps to form a better match to a previous study using ranked data.

20. Spearman’s Rho Scores in the left panel are rank ordered on the right.

21. Spearman’s Rho Scores in the left panel are rank ordered on the right. Ranks Of 2 & 3 have a Mean = 2.5

22. Spearman’s Rho Finally, we could compute Spearman’s rho on the ranks: Spearman’s rho = .973 We will NOT manually compute Spearman’s Rho this semester.