testing for differences Flashcards
what is cohen’s d?
- measures the effective size by measuring the differences between two sample means
- takes the standard deviation into account as well
how do you calculate cohen’s d for a population or a sample?
- calculate the mean SD
pop = s.d(1) +s.d(2)/2
sample = s(1) + s(2)/2 - calculate cohen’s d
pop = mean(1)-mean(2)/mean SD
sample = m(1)-m(2)/mean SD
the bigger the cohen’s d….
the larger the difference, the less overlap of scores there are between two samples, meaning there was a larger effect
what would be considered a small cohen’s d value?
0.2
what would be considered a medium cohen’s d value?
0.5
what would be considered a large cohen’s d value?
0.8
degrees of freedom: one sample t-test
N-1
degrees of freedom: paired t-test
N-1
degrees of freedom: independent groups t-test
(Na-1) + (Nb-1)
degrees of freedom: pearson’s r
N-2
degrees of freedom: chi square 1 variable
no of categories-1
degrees of freedom: chi square 2 variable
(no of rows -1) x (no of columns -1)
parametric tests (2)
- find smaller details about effects in data
- assumes - normal distribution, no extreme scores and variances of samples/populations roughly equal
non-parametric tests
- focus on ranks not scores
- sample sizes may not be small, variances may not be equal, data may not be normally distributed
what is the non-parametric alternative to the independent t test?
mann-whitney U
what is the non-parametric alternative to the paired/related t test?
wilcoxon signed rank
what is the non parametric alternative to pearson’s r?
spearman’s rho
how to conduct a pearson’s r test
- calculate mean and s.d for group X and group Y
- calculate how far each score deviates from its group mean
- multiply x and y deviations together and add up all the values in this column
- calculate the sample covariance by doing: total covariance/n-1
- r = sample covariance/s.dX times s.dY
- df = N-2
how to conduct a spearman’s rho test
- convert data into ranks - separate for each group
- calculate the difference in ranks for each group - i.e RANKx-RANKy
- square the differences. add this column together
- spearman’s rho: (1-value from S3)/n(n2-1)
- where N is the size of the X or Y sample in a related condition
how to conduct a 1 variable chi-squared test
- calculate expected fr: total number of values/total number of categories
- calculate difference score: expected-actual
- square the differences
- squared frequency/expected frequency
- chi = sum of squared frequencies/expected frequencies
- df = no of categories-1
how to conduct a 2 variable chi squared test
- calculate the expected frequency -
a. add up the values in column A (C1), and column B (C2)
b. add up the values in row A (R1) and row b (R2)
c. for each box, multiply the the column total*row total/total number of people in A and B - calculate (expected-observed)2 for each value
- (expected-observed)2/expected for each value - sum all together
- df = (no of rows -1)*(no of columns-1)
how to conduct a mann-whitney U test
- replace all scores with ranks - take ties into account
- sum ranks for each group
- calculate the smallest possible rank sum for each group by doing: n0.5(N+1)
- rank sum - rank minimum for each group
- U = the smaller value
how to conduct a wilcoxon signed rank test
- calculate difference in condition scores
- if difference is a negative value, assign it a ‘-1’, is difference is positive, assign it ‘+1’, if there is no change, assign it ‘0’
- diff score*sign value for each value
- rank all these values, not including 0 and taking ties into account
- create a positive and negative difference columns - for ranks that came from a positive difference value, put them in the positive difference column, for ranks that can from a negative difference value, put them in the negative difference column.
- calculate the sum of each of these columns.
- t = sum of the least occurring sign
