    Chapter 6: Analysing the Data Part III: Common Statistical Tests # Steps in hypothesis testing for correlation

We will formally go through the steps described in the previous chapter to test the significance of a correlation using the logical reasoning and creativity data

### Step 1: Null hypotheses

Ho: = 0.0

H1:  0

Notice the hypotheses are stated in terms of population parameters. The null hypothesis specifies an exact value which implies no correlation. The alternative is two-tailed. We set the alpha level at .05.

### Step 2: Assumptions

Howell describes the assumptions associated with testing the significance of correlation (pp. 232). These refer to normality and homogeneity of variance in the array of possible values of one variable at each value of the other variable. These assumptions are difficult to test. A close approximation is if the normality of both variables is approximately normal. Without evidence to the contrary we will assume these assumptions are OK.

### Step 3: Calculate the test statistic

SPSS using the screens and options identified in the SPSS screens and Outputs booklet gives us the output shown in Output 6.1.

### Step 4: Evaluate the statistic.

From the output we determine that the correlation of .736 is significant at the .001 level. We infer that the null hypothesis is too unlikely to be correct and we accept the alternative as a more likely explanation of the finding. The summary statement is as given before r(18) = .736, p < .001.

### Step 5: Interpret result

First we can say that there was a significant positive correlation between scores on the logical reasoning test and scores on the creativity test (r(18) = .736, p < .001). Logical reasoning accounts for 54% of the variability in creativity scores. The positive correlation implies that higher scores on creativity tend to go with higher scores on creativity and lower scores on logical reasoning go with lower scores on creativity.

Second, we might like to speculate about how logical reasoning might be related to creativity. We cannot say from the above that logical reasoning causes creativity but we might be able to speculate that both cognitive abilities share commonalities. Both might be caused by higher intelligence. People with higher intelligence are better at both logical reasoning and creativity because they can entertain a larger range of possible options when it comes to creative tasks.

Notice how the first interpretation stays close to the specific variables that were measured but the second moves away from the specific variables that were measured to discuss the psychological constructs that were operationalised in the first place. Obviously this is the most controversial part of the whole process but the part we are mostly interested in.

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