Magnitude, independent r, regression Flashcards
How do we calculate the effect size for the following analyses:
t-test?;
ANOVA?
Correlation?
Cohen’s d;
Omega square;
r square
How do we assess association/effect for chi-square?
phi (for a 2 x 2 contingency table); correlation between two dichotomous variables; interpreted as Pearson’s r
If a sample size is large enough, very small effects in a chi-square test will be detected as what?;
So we convert chi-square to what?
Significant;
Phi: a measure of association that tells you how big the effect is (if chi-square is significant, so is phi)
What is Cramer’s phi?;
What’s the formula?;
Why would you get the same value if you used this formula for a 2 x 2 contingency table?
A generalisation of phi to r x c tables; a measure of association between two variables
Cramer’s phi = square root of chi-square divided by N (k-1);
Because for a 2 x 2 contingency, k-1=1 so it’s the same as dividing by N
How can Cramer’s phi be interpreted?;
How would you interpret an effect size of small, medium & large in a 2 x 2 contingency table?
In terms of Cohen’s conventions; although it’s not actually measuring effect size, the concepts are related;
Small: .10; medium: .30; large: .50
When calculating Cramer’s phi in a chi-squared test for independence, what does k equal?
smaller of row or column (e.g. in a 2 x 3 table, k would be 2)
What does testing the difference between two independent r’s compare?;
When is this technique applicable?
The size of two correlations;
Only if the two correlations are independent (i.e. different people in each group)
State the statistical hypotheses;
Null: rho1 - rho2 = 0 or rho1 = rho2; Alternative: rho1 - rho2 /= 0 or rho1 /= rho2;
Why do we need to convert the value of r to compare correlations for two independent groups?;
What do we convert it to?
To transform r to a value that is normally distributed & standardised; when null is rho = 0, r is normally distributed around zero; but when null is rho1 = rho2, sampling distribution is skewed;
Fischer’s r prime (or r to z); it’s approx normally distributed around rho prime (transformed value of rho) with standard error Sr prime (1 / square root of N-3)
What is the process of testing the difference between two independent r’s?
Covert each r to r prime (using Fischer’s table); calculate z (r1 prime - r2 prime / standard error of difference: square root of 1 / (N1 - 3) + 1 / (N2 - 3)); compare with z crit (+/-1.96)
What formulas do we use when testing the hypothesis that rho equals a specific value?
Sr prime = square root of 1 / n - 3 (standard error of difference); z = r prime - rho prime / Sr prime
Describe some factors that influence r
Non-linear relationship; restriction of range; extreme scores; heterogeneous subsamples (data which could be subdivided into two distinct sets on the basis of some other variable)
What are the goals of correlation coefficients?
To obtain an estimate of rho (reliability & validity estimates); use in other analyses (basis of factor analysis, multiple regression & SEM); calculate coefficient of determination (r squared - variance accounted for); prediction
What is regression?
Where the correlation between two variables, X & Y, is used to predict scores on Y from our knowledge of X
What is the X variable called?;
What is the Y variable called?
Predictor;
Criterion
