Presentation on theme: "Correlation, Reliability and Regression Chapter 7."— Presentation transcript:
Correlation, Reliability and Regression Chapter 7
Correlation Statistic that describes the relationship between scores (Pearson r). Number is the correlation coefficient. Ranges between +1.00 and –1.00. Positive is direct relationship. Negative is inverse relationship. .00 is no relationship. Does not mean cause and effect. Measured by a Z score. Generally looking for scores greater than.5
Reliability Statistic used to determine repeatability Number ranges between 0 and 1 Always positive Closer to one is greater reliability Closer to 0 is less reliability Generally looking for values greater than.8
Scattergram or Scatterplot Designate one variable X and one Y. Draw and label axes. Lowest scores are bottom left. Plot each pair of scores. Positive means high on both scores. Negative means high on one and low on the other. IQ and GPA? ~ 0.68
Pearson (Interclass Correlation) Ignores the systematic bias Has agreement (rank) but not correspondence (raw score) The order and the SD of the scores remain the same The mean may be different between the two tests The r can still be high (i.e. close to 1.0)
What is a Mean Square? Sum of squared deviations divided by the degrees of freedom (df=values free to vary when sum is set) SSx = sum of squared deviations about the mean which is a variance estimator
Running ICC on SPSS Analyze, scale, reliability analysis Choose two or more variables Click statistics, check ICC at bottom Two-way mixed, consistency Use single measures on output
Interpretation (positive or negative) <.20 very low .20-.39 low .40-.59 moderate .60-.79 high .80-1.00 very high Must also consider the p-value
Correlation Conclusion Statement 1. Always past tense 2. Include interpretation 3. Include ‘significant’ 4. Include p or alpha value 5. Include direction 6. Include r value 7. Use variable names There was a high significant (p<0.05) positive correlation (r=.78) between X and Y.
Coefficient of Determination Represents the common variance between scores. Square of the r value. % explained. How much one variable affects the other
R 2 the proportion of variance that two measures have in common-overlap determines relationship-explained variance
Partial Correlation the degree of relationship between two variables while ruling out that degree of correlation attributable to other variables
Simple Linear Regression Predict one variable from one another If measurement on one variable is difficult or missing Prediction is not perfect but contains error High reliability if error is low and R is high
Residual is vertical distance of any point from the line of best fit (predicted) r=.93 Positive and negative distances are equal
Prediction Y=(bx)+c Y is the predicted value B is the slope of the line X is the raw value of the predictor C is the Y intercept (Y when x = zero) Y vertical/X horizontal
Prediction Y p = (bx)+c HT p = (.85x80)+(108.58) HT p = (68)+(108.58) HT p = 176.58 Residual (error) = diff between predicted and actual Subject must come from that population! HTWT 185.0080.00 185.0087.00 152.5052.00 155.0064.10 172.0066.00 179.0081.00 160.0067.72 174.0076.00 154.0060.00 165.0070.00
Standard Error of the Estimate (SEE) is the standard deviation of the distribution of residual scores Error associated with the predicted value Read as a SD or SEM value 68%, 95%, 99% SEE x 2 then add and subtract it from the predicted score to determine 95% CI of the predicted score. SEE SEE = the square root of The squared residuals Divided by the number of pairs
Prediction Y p = (bx)+c HT p = (.85x80)+(108.58) HT p = (68)+(108.58) HT p = 176.58 SEE x 2 = 19.5 95% CI = 157.08 – 196.08 HTWT 185.0080.00 185.0087.00 152.5052.00 155.0064.10 172.0066.00 179.0081.00 160.0067.72 174.0076.00 154.0060.00 165.0070.00
Multiple Regression Uses multiple X variables to predict Y Results in beta weights for each X variable Y=(b 1 x 1 ) + (b 2 x 2 ) + (b 3 x 3 ) … + c
SPSS - R Prediction Y=(WT x.40) - (skinfold x 1.04) + 156.45
Next Class Chapter 8 & 13 t-tests and chi-square.
Homework 1. Make a scatterplot with trendline and r and r 2 of two ratio variables. 2. Run Pearson r on four different variables and hand draw a scatterplot for two. 3. Run ICC between VJ1 and VJ2. 4. Run linear regression on standing long jump and predict stair up time. Work out the equation and CI for subject #2. 5. Run multiple regression on subject #2 and add vjump running, circumference and weight to predictors. Also out the equation and CI.