CHAPTER 14
why is using the coefficient of determination a better measure of accuracy?
- a correlation coefficient used alone can give a false impression of strength. for instance, a correlation of r = .50 may seem to be a moderately strong correlation because it falls right in the middle of 0 and 100. However, when we compute the coefficient of determination, we find that only 25% of the variability of the scores can be predicted from this relationship. Thus, COEFFICIENT OF DETERMINATION OR r^2, IS A MUCH BETTER MEASURE OF STRENGTH AND ACCURACY OF OUR PREDICTION THAN the correlation coefficient alone
Cause and Effect Consideration
- a correlation that exists between two variables does not necessarily mean that one causes the other - sometimes relationships exist because of the effect of other outside influences ex: if we found positive relationship between self-esteem and grades, we could not conclude that high or low self-esteem cases students to earn high or low grades; they may influence each other in a reciprocal fashion or outside influences such as parenting - although these causal relationships cannot be confirmed sing the method of correlation, it would also be incorrect to say tat the variables involved are definitely not causally related - causal relationships can be demonstrated only through experimentation
correlation coefficient
- a statistical formula that determines the direction and strength of a relationship - ranges from -1.00 to +1.00
Restricted Range Consideration
- caution should be given when interpreting correlations from a restricted range versus a full range of scores - the problem with restricting the range occurs when a sample is used that limits the scores on one or both variables more than would be found in the population ex: car sales manager using assessment to all current employee,rather than all employee even those who are no longer employed
a negative correlation
- exists when two variables are changing together in OPPOSITE directions - +/- or -/+ - inverse relationship
a positive correlation
- exists when two variables are changing together in the SAME direction - +/+ or -/-
direction of relationship
- indicated by sign +/-
strength of relationship
- indicated by the absolute numerical value of the correlation coefficient - the STRONGER THE CORRELATION, THE CLOSER THE NUMERICAL VALUE WILL BE TO 1.00, regardless of the sign
Correlation research
- involves using statistical procedures to analyze the relationship of two variables
Validity
- measuring the degree to which a test measures what it is supposed to measure; for newly developed assessment instruments ex: testing new assessment instrument to measure depression should have scores demonstrate a positive correlation with scores on other standardized measures of depression
Prediction
- one of the main uses of the Pearson correlation - if there is a strong relationship between variables, then knowing the score on one variable will enable us to predict the score of the other variable - the stronger the relationship, the more accurate the prediction will be ex: we could probably predict with some degree of accuracy of students' grades on a test by knowing how many absences they have had (there is a negative correlation)
Outliers
- scores on either the X or y variable that are extreme in comparison to most other scores - located by visually inspecting the scatterplot - caution is advised in interpretation because outliers can have a dramatic effect on the magnitude of the correlation
coefficient of nondetermination
- tells us the proportion of the variability that is NOT COMMON VARIANCE and that is RELATED FACTORS DO NOT INFLUENCE BOTH SETS OF SCORES - calculated by subtracting r^2 from 1; 1-r^2 - one variable's variance doesn't explain the variance of other
alternative hypothesis of Pearson Correlation
- the alternative hypothesis can be two (nondirectional) or one tailed (directional) - a nondirectional alternative hypothesis merely asserts that a NONZERO correlation in the population and calls for two tailed test; positive or neg r values; Hi: p=/ 0 - a directional alternative hypothesis specifies either a positive or negative correlation and calls for a one tailed test; the obtained r value must be significant and in the direction specified before Ho may be rejected; Hi: p> 0 or Hi: p<0
null hypothesis of Pearson Correlation
- the null hypothesis states that no signifcant relationship exists between two variables, that any correlation found is simply due to chance - Ho: p=0 (no correlation in population)
coefficient of determination
- the proportion of variance that two variables have in common - computed by squaring r, r^2 - if there is a correlation between two variables, then the scores tend to change together in predictable ways - this is the shared common variance between the scores that is assumed to be influenced by the same factors
criterion variable
- the variable that is estimated from predictor variables
Reliability
- used to assess the reliability of testing instruments - reliability refers to the consistency or stability of test scores upon repeated administrations of the test ( or alternate version) ex: if you take a personality test that says you're an introvert, it should say the same results two months later
Pearson product moment correlation
- used to examine linear relationships between variables measured on interval or ratio scales
regression analysis
- using obtained scores on one variable to predict unknown scores on another variable based of a correlation existing between those two variable ex: making predication as the heights of 21 yr olds based on their heights at age 12 or predicting college GPA from high school GPA
predictor variables
- variables used to estimate values on another variable ex: high school GPA for college GPA or SAT scores
Uses of the Pearson Correlation
1) Validity 2) Reliability 3) Prediction
y-intercept
a, is the point where the regression line cuts across or intercepts the Y-axis
slope
b, tells us how much and in what direction the regression line slants
regression line
line of best fit
