Correlations

Correlation

• how two variables covary in relation to each other

  • how they move together/vary together

• standardized covariance

• the value of r can range between -1 and +1

  • - = move in opposite directions

  • + = move in the same directions

• if r = 0 — there is no linear relationship between the two variables

• the closer r is to ± 1, the stronger the relationship

• if r = ±1 — there is a perfect linear relationship between the variables

Deviation from the Mean

• Observation - mean = distance of the observation from the mean

Two ways to define correlation coefficient

• z scores

• covariation

z scores

• z = 0 — score = mean

• z > 0 — score ≠ mean

• z = 1 — score = 1 SD from mean

• z = 1 — score = 2 SD from mean

Variance Formula

Covariance Formula

Coefficient Determination

• r² indicates the percent of the variability in y that is accounted for by the variability in x

Model

• variability in scores that we can account for

Error

• variability in scores that we cannot account for

t obtained formula

Steps in Finding Correlation

1. create H0 and H1

2. set parameters (find critical t)

3. calculate t obtained

4. compare critical t and t obtained

5. find p-values in SPSS

Steps in Finding Confidence Intervals

1. convert Pearson’s r to z score

2. compute a confidence interval for z score

3. convert z score back to Pearson’s r

Calculating Confidence Intervals

• CI = value ± (z critical (SE))

Standardization Formula

Reliability

• in research, the term reliability means “repeatability” or “consistency”

• a measure is considered reliable if it would give us the same result over and over again (assuming that we are measuring isn’t changing!)

Internal Consistency Reliability

• AKA “coefficient alpha”, “Cronbach’s alpha”, “reliability coefficient”

• judge the reliability of an instrument by estimating how well the items that reflect the same construct yield similar results

• looks at how consistent the results are for different items for the same construct within the scale

  • questionnaires often have multiple questions dedicated to each factor (some need to be reverse coded)

Purpose of Internal Consistency Reliability

• used to assess the consistency of results across items within a test

• how well do the items “hang” together?

• typically, a reliability analysis is done on items that make up a single scale (items all supposed to measure roughly the same construct) — founded on correlations of items

Reliability Coefficients

• range from 0-1.00 with higher scores indicating the scales is more internally consistent

• generally, reliabilities above .70 are considered acceptable for research purposes

• reliability analyses are carried out on items AFTER recoding (reverse coding)

Validity

• is the test measuring what it claims to measure