19.
The Statistical Significance of a Correlation Coefficient
A correlation is statistically significant if it is unlikely that you could have gotten a correlation as big as you did if in fact there was no relationship between variables.
If the probability (p) is less than some small degree of probability (e.g., 5% or 1%), the correlation is considered statistically significant.
A person’s predicted Z score on the criterion variable is found by multiplying the standardized regression coefficient ( ) by that person’s Z score on the predictor variable.
Formula for the prediction model using Z scores:
Predicted Z y = ( )(Z x )
Predicted Z y = predicted value of the particular person’s Z score on the criterion variable Y
Z x = particular person’s Z score in the predictor variable X
So, let’s say that we want to try to predict a person’s oral presentation score based on a known relationship between self-confidence and presentation ability.
Which is the predictor variable (Zx)? The criterion variable (Zy)?
26.
Example of Prediction Using Raw Scores: Change Raw Scores to Z Scores
From the sleep and mood study example, we known the mean for sleep is 7 and the standard deviation is 1.63, and that the mean for happy mood is 4 and the standard deviation is 1.92.
The correlation between sleep and mood is .85.
Change the person’s raw score on the predictor variable to a Z score.
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