This is a draft cheat sheet. It is a work in progress and is not finished yet.
One-Way ANOVA
Between-Group Mean Square |
Within-Group Mean Square |
F-Ratio |
1) (Subtract overall mean of pop from each group’s mean)2 |
1) (subtract overall mean of pop from each group (sample) mean), |
1) [(between group mean square) / (w/in-group mean square)] |
2) (squared difference) (sample size) |
2) then multiple each difference by (n-1) |
2) if ~ 1, then btwn-groups & w/in-groups variances similar, accept H0 |
3) compute degree of freedom (number of groups minus 1) |
3) calculate the grand sum |
3) if >1, then reject H0 |
4) calculate between-groups mean square = [(btwn-group variance) / (df)] |
4) calculate the degrees of freedom total (N-n of groups) |
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5) calculate the w/in groups mean square = [(sum of squares) / (degrees of freedom total)] |
- Analysis of Variance ( compares means between 3+ samples)
Does not indicate which group(s) are different from which other groups (s)
- Parametric test
- Bonferroni post hoc test, reveals which specific means differed. Use if ANOVA was sig. using for pairwise comparison
- It multiplies each of the significance levels from the LSD test by the number of tests performed. If this value is greater than 1, then a significance level of 1 is used.
Chi-Square Test
1) calculate the expected frequency (E) = [(row total) (column total) / total sample N] |
Standardized Residuals |
Phi (Ф) |
Cramer's V |
2) for each cell, find (difference between overserved & expected counts)2 |
reveal what cell adds the most statistical value to the test. |
to measure the strength of association of chi-square test |
to measure the strength of association of chi-square test |
3) divide square difference by expected count for each cell, then sum results |
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2x2 table |
greater than 2x2 table |
4) df = [(n of rows -1) (n of columns -1)] |
5) check X2 table for significance at @ 0.05 alpha level |
- Dependent & Independent nominal/nominal or nominal/ordinal data
- H0= no relationship between variables; expected counts for each cells = observed counts
- n is greater/equal to 20; no expected frequencies less/equal to 5 in 20% or more of the cells
Fisher's Exact Test for Chi-Square
-Use when Chi-Square assumptions are violated (>20%)
- Very small samples |
Spearman's Rank Correlation
1) Turn raw scores into ranks |
Rho varies from -1 to +1 |
2) find d2 = (difference between rankings)2 |
-1 (a perfect negative correlation; as X increases, y decreases) |
3) add up all the data in d2 column to obtain sumd2 |
0 = no association |
4) calculation spearman’s rank correlation coefficient (rho) rs = [1- (6*sumd2)/N3-N)] df= n-2 |
+1 (a perfect positive correlation; as X increases, Y increases |
- Measures of associate for two ordinal variables; whether a relationship exists, how strong it is, what is the direction/pattern of relationship) (what happens to one variable, happens to the other variable)
- Nonparametric version of Pearson correlation coefficient
- H0= no sig
independent = x ; dependent = y
Pearson's R Correlation Coefficient
r= Rho = measure of association (-1 to +1) |
assumes x and y is normally distr. & linearly related |
(Pearson’s r)2 = PRE stat (strength of predicting amount of variance in Y based on X) |
r2 = % of variance in dependent (Y) explained by independent (X) |
usually interval/ratio level data
Parametric vs. Non-parametric Tests
Parametric |
Non-Parametric |
interval or ratio data |
nominal and/or ordinal data |
one-way ANOVA |
Distribution free |
Pearson's R Correlation Coefficient |
Wilcoxon Signed-Rank Test for Two Related Conditions |
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Mann-Whiteny U Test for Two Independent Conditions |
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Wilcoxon Rank Sum Test for Two Independent Conditions |
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Chi-Square Test |
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Kruskal-Wallis |
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Spearman's Rank Correlation |
Wilcoxon Rank-Sum & Mann-Whitney U tests
nonparametric equivalent of independent-sample t-test |
nominal and/or ordinal data |
Tests two independent conditions
Wilcoxon Signed-Rank
- Use this test for two related conditions (paired, matched)
- ordinal data
- nonparametric equivalent to the dependent-sample t-test
H0 = The two groups are identically distributed. |
Kruskal-Wallis
nonparametric equivalent of one-way ANOVA |
nominal or ordinal data, but more than two independent samples |
uses chi-square distribution |
Regression
Predicts dependent (y) based on value of independent (x) |
Regression Formula: line that makes the sum of squares of the vertical distances of the data points from the line as small as possible |
Principle of least-squares - finds estimates of parameters in a stat model based on observed data |
y= a + bx; a= y-axis; b= slope |
interval/ratio level data
assumes linear relationship
observes independent (x)
Correlation
Tests for |
Difference between (r) and (r)2 |
Assumptions |
How well X predicts Y |
r= Pearson's correlation coefficient = measure of association |
For each independent (x), dependent (y) must be normal |
how “tightly the predicted values fit regression line |
r2 = PRE stat (strength of predicting amount of variance in Y based on X) |
Dependent variable variances same for all independent values (homoscedasticity) |
to what degree X covaries with Y |
r2 = % of variance in dependent (Y) explained by independent (X) |
Avoid predictions outside the observed values; beware extremes; relationships must be linear over all values. |
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linear relationship, observes independent (X) |
usually, interval/ratio level data
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