Final Flashcards
Repeated-Measures ANOVA
- used when? (2)
- independant assumption violated
- 3+ conditions
Repeated Measures ANOVA
- SS calculated? (4)
SStotal
SSwithin treatments
SSsubjects
SSerror
Repeated Measures ANOVA
formulas:
- SS total
- SS within treatments
- SS subjects
- SS error
SS total = Σx2 - (Σx)2/N
SS <strong>within treatments</strong> = n Σ(x̄w - x̄)2
SS subjects = k Σ(x̄s - x̄)2
SS error = SStotal - SSwithin treatments - SSsubjects
Repeated Measures Anova
- MS formulas
- df formulas
MStreatment
dftreatment = k - 1
MSerror
dferror = (k-1)(n-1)
When calculating SSerror, eliminates effects of MSsubjects
Repeated Measures Anova
- assumptions (2)
1) Normality
2) Sphericity
Repeated Measures ANOVA ASSUMPTIONS
2) Sphericity
assumption of equal variances & equal covariances
(NOT robust to violations)
Factorial ANOVA
- simplest case?
2 b/w-subject IVs of 2 levels
Main effect
mean difference among levels of one factor
Interaction
mean differences between treatment conditions (cells) are different from what would be predicted from overall main effects of factors
- effect of one factor depends on different levels of 2nd factor
Two-Factor ANOVA
(3) hypothesis tests?
1) main effect of A
2) main effect of B
3) A x B interaction
Two-Factor ANOVA
- SS
SS total
SS BG
SS WG
SS A
SS B
SS AxB
Two Factor ANOVA
Formulas:
- SS total
- SS BG
- SS WG
- SS A
- SS B
- SS AxB
SS total = ΣXtotal2 - ( ΣXtotal)2/N
SS BG = ΣT2/n - G2/N
SS WG = SST - SSBG
SS A = ΣTrow2/nrow - G2/N
SS B = ΣTcolumn2/ncolumn - G2/N
SS AxB = SSBG - SSA -SSB
Two-Factor ANOVA
- MS
- df
- F
MS for:
- A → a -1
- B → b -1
- AxB → (a-1)(b-1)
- WG → ab(n-1)
F = MS/MSWG
- FA, FB, FAxB
Correlation
describes linear relationship between 2 ordinal/interval level variables
Correlation
- relationship must be?
- restricted range & reliability of measures limits…?
1) linear
2) magnitude of correlation coefficient
Correlation
- (3) assumptions
1) Normality
2) Linearity
3) Homoscedasticity
Correlation ASSUMPTIONS
3) Homoscedasticity
assumes variance around regression line is same for all X values
(equal spread)
Regression
technique to fine line of best fit
Correlation suggests we can….
predict Y values for given values of X
If correlation is perfect, all points will..
If NOT?
- If correlation is perfect, all points will*..fall on regression line
- If NOT,* regression line must be calculated.
Regression
Notation for:
- predicted values of Y
- residuals
- regression coefficient (slope)
- Y intercept
1) Y’
2) Y-Y’
3) b1
4) bo
Regression
- residuals
errors of underprediction & overprediction
Sum of squared residuals is?
Minimal
(regression line = best-fitting line)
Regression
- formula for predicted values of Y (Y’)
Y’ = b1x + bo
Correlation & Regression
formulas:
- b1
- bo
b1 = r (Sy/Sx)
bo = y-bar - b1 x̄
Correlation & Regression
calculate?
- r
- b1
- bo
- Y’
- SSY<strong>’</strong> = Σ(Y’-Ybar)2
- SSY-Y’ = Σ(Y-Y’)2
- MSpredicted
- MSresidual
- Fobtained
Regression
- predicted/explained variance
Variability in Y predicted by X
SSY’ = Σ(Y’-Ybar)2
Regression
- Residual/Error Variance
Variability in Y NOT predicted by X
Non-Parametric Tests
make no assumptions about shape of distribution
Chi-Square Test for Goodness of Fit
- uses?
- determines?
uses sample data to test hypothesis about shape/proportion of population distribution
- determines how well sample proportions fit population proportions specified by null hypothesis
Chi-Square Test for Goodness of Fit
- null hypothesis
- alternative hypothesis
Ho: change in frequency due to chance
H1: change in frequency NOT due to chance
Chi-Square Test for Goodness of Fit
- formula
- df?
X2 = Σ [(o - e)2/e]
df = c -1
- c = # of categories
Chi-Square Test for 2 Independent Samples
used to test whether there is association between 2 frequency variables
Chi-Square Test for 2 Independent Samples
- null & alternative hypotheses
Ho: treatment is independant of outocme
H1: treatment is NOT independant of outocme
Chi-Square Test for 2 Independent Samples
- formula
- df?
X2 = Σ [(o - e)2/e]
e = [(R)(C)]/N
df = (R-1)(C-1)
