Using SPSS to Understand Research and Data Analysis.

8.3 Interpreting the Output

The output file contains a matrix of all possible correlations among the variables (Figure 8.3).

The four variables (highlighted blue) are listed in rows as well as in the columns (thereby creating the matrix of all possible correlations). In each cell (or "box") of this matrix are three rows.

• The first row contains the Pearson r value (highlighted yellow)
• The second row contains the two-tailed probablility (Sig., highlighted purple)
• The third row shows the number of pairs of scores on which each r value is computed.

Next note that the r value for the correlation between each variable and itself (e.g., Social Skills 1 with Social Skills 1) equals 1. This is because the correlation of any variable with itself is perfect - something of no interest, so these boxes can be ignored.

Also note that the 1's form a diagonal cutting from the upper left to the lower right of this matrix. Note also that all of the correlations listed below the diagonal are duplicates of the correlations shown above the diagonal. So we need only pay attention to the six correlations shown above the diagonal to interpret our output, since the information below the diagonal is redundant.Last, note that asterisks are placed next to the r values for which the probability is less than or equal to .01 to flag these as statistically significant correlations.

Now we can begin intepreting the degree and direction of the relationships indicated by the six correlation coefficients of interest. Recall that the direction is easily seen by the sign of the r value (+ or -). A positive correlation indicates that high scores on one variable are associated with high scores on the second variable, while a negative correlations indicates that high scores on one variable are related to low scores on the second variable. All of our signficant correlations are positive in this example, so we will discuss the more complex issue of interpreting degree of relationship.

There are two ways to intepret the degree of relationship. The first is an all or none judgment of whether or not the variables are significantly related. The null hypothesis (Ho) is that r = 0.0, meaning that the variables are unrelated (hence, the degree of relationship is zero). Recall the convention is:

• If the Sig., or probability (p), associated with the r valuef .05 or less, then we reject Ho, and conclude that there is a statistically significant relationship between pair of variables.
• If p > .05, then we retain Ho, and conclude that the variables are unrelated.

Thus, if the Sig. value listed for a correlation is .05 or less, we can assume that the correlation is not the result of chance or random sampling error. That is why we would reject Ho and conclude that the correlation is a real one, and thus, one that can be generalized from the sample to the overall population in which we are interested.

So to interpret our correlation matrix, we first need to look at the Sig. values (p) listed below each r value (recall that SPSS makes this easier by flagging correlations for which p < .05, placing asterisks next to the r values). Examining these, we see that four of the six correlations are significant. The nonsignificant correlations are between Social Skills and masctot (r = .12, p = .06), and between masctot and femtot (r = -.06, p = .35). Thus, our first conclusions concern the nonsignificant correlations. We can conclude that employees' social skills are unrelated to their masculinity, and their degree of femininity is unrelated to their masculinity.

The latter conclusion is of theoretical interest, because intuitively one might have expected masculinity and femininity to be significantly correlated in a negative direction (high masculinity would be related to low femininity). The fact that the correlation is not significant supports the proposition that these variables are independent, and that it is possible to have all combinations of low/high levels of masculinity and femininity.

Recall that the concept of androgyny implies that these variables are independent. That is, it possible to score high or low on one variable and either high or low on the other. For example, androgynous individuals score high on both, while sex-typed persons score high on one, but low on the other). Thus, this nonsignficant correlation supports the theory of androgyny.

Turning to the four significant correlations, note that although they are all significant, the r values vary widely - the coefficients range from .68 (the strongest) to .28 (the weakest). Beyond the all-or-none decision about statistical signficance, researchers also often elaborate on the degree of relationship. While there are no hard-fast rules, here is a general rule of thumb:

• r values greater than .50 indicate a strong correlation
• r values around .30 indicatea moderate correlation
• r values less than .20 indicate a weak correlation

The import of this is that it is possible for two variables to be significantly related (statistically), even if the relationship is a weak one. Thus, researchers typically expect a statement of degree to modify the basic conclusion that a relationship is statistically significant.

Using the above guidelines looking across the first row of the matrix, we can conclude that there is a moderate positive relationship between social skills and task skills (r = .30, p = .000), and a strong postive correlation between social skills and femininity (r = .62, p = .000). Thus, a higher degree of social skills is related to both a higher degree of task skills and higher femininity, but the latter is a much stronger relationship.

Looking in the second row, we can conclude that there is a moderate positive relationship between task skills and femininity (r = .28, p = .000), and a strong positive correlation between task skills and masculinity (r = .49, p = .000). Thus, a higher degree of task skills is related to both higher femininity and higher masculinity, but the latter is a much stronger relationship.

So these analyses have confirmed some expectations, but not others. It is perhaps not surprising that the strongest positive correlations were obtained between masculinity and task skills and between femininity and social skills. Task skills in leadership are associated with instrumentality, a stereotypically masculine characteristic. And Social skills in leadership are associated with expressiveness, a stereotypically feminine characteristic.

However, it is interesting to note that although masculinity was unrelated to social skills, the correlations between femininity and task skills was moderate and statistically significant. Thus, masculinity was strongly related to task skills, and masculinity was independent of social skills (as one might have intuited). However, while femininity was strongly related to social skills, it was not unrelated to task skills (as one might have expected based on social stereotypes).

Confused? We are still in the preliminary stages of identifying the pieces of the puzzle, so we don't yet have the larger picture in front of us. The relationships will become clearer as we carry out other kinds of analyses in the succeeding chapters. However, this first run has generated some interesting correlations that suggest what kinds of characteristics seem to go together in EZ employees. You will discover some similar types of relationships in the exercise to follow, and you are encouraged to explore other correlations in the data file on your own!