MRM2
1. Conceptual models & Analysis of Variance
Variables
PV = Predictor Variable
(IV = Independent Variable)
OV = Outcome Variable
(DV = Dependent Variable)
Quantitative Categorical
! Labels
Discrete (only distinct points on a scale)
Nominal (no meaning in order, just naming)
Interval (difference between two values is meaningful)
Ordinal (e.g. from low to high height)
Ratio (absolute 0)
!It is a count but no calculation (mean, median, interquartile
range etc.)
p-value (probability)
! if p-value low (<0.05), H0 must go (reject)
Conceptual Models
! Visual representations of relations between theoretical constructs (and variables) of interest
Moderation
One DV (Student satisfaction)
Two IVs (Commitment of teacher and communication skills)
!One variable moderates the relationship between two other variables
!When proposed effect is stronger in certain settings
!Moderation=Interaction
Mediation
A affects B and is affected by C
!When proposed relationship “goes via” another variable
! One variable mediates the relationship between two other variables
One-way ANOVA (Analysis Of Variance)
! Comparing groups (on quantitative variable, explained by PV/IV)
! How much of the variability of the independent variable is explained by the dependent variable
or
! Comparing the variability between the groups against the variability within the groups
Variance = the average of the squared differences from the mean (average)
Sum of Squares = the sum of the squared differences from the mean (average)
! Use of square in order to avoid negative values
,In Anova only one independent and one dependent variable:
- DV/OV has to be quantitative
- IV/PV has to be categorical with more than two groups
Pre Conditions / Assumptions:
- Variance is homogenous across groups (Leven’s Test)
! If not: Welch’s ANOVA
- Residuals are normally distributed
! If not: Kruskal-Wallis test
- Groups are roughly equally sized
- Subjects can only be in one group (between subjects design)
! If not: Repeated-measures ANOVA
1. Mean of all observations
2. Total sum squares
! General average (regardless groups)
3. Model sum of squares (Difference between the groups)
! Average of each group
! Difference is desired to be higher because (as difference between the group)
4. Residual (Differences within the groups)
! Square of the differences within a group
! Difference within the group is desired to be lower (as should be homogenous groups)
!Proportion of the total variance in data
, st
F-test (1 step)
! To investigate if the group means differ with an ANOVA
(Model/Residual)
Degrees of Freedom
! In order to find out ‘mean square’
!
Then compare value to f-table
Based on p-value reject or accept H0
EXAMPLE:
!Conclusion:
There is a statistically significant difference (p < .05)
between at least two of the groups
nd
Multiple Comparisons (2 step)
! To define which groups differ
- Statistically comparing each individual group’s scores against each one another
- Significance (alpha) at 0.05 (=5%), so Confidence level at 0.95 (=95%)
- P(Type I error) = 5%
- Multiple comparisons cause artificial inflation of alpha
- So we “adjust” for that. All post hoc tests are adjustments for this
- “Bonferroni” divides the alpha over all comparisons.
! 5 comparisons? Each gets 1%. So good if you have few comparisons
1. Conceptual models & Analysis of Variance
Variables
PV = Predictor Variable
(IV = Independent Variable)
OV = Outcome Variable
(DV = Dependent Variable)
Quantitative Categorical
! Labels
Discrete (only distinct points on a scale)
Nominal (no meaning in order, just naming)
Interval (difference between two values is meaningful)
Ordinal (e.g. from low to high height)
Ratio (absolute 0)
!It is a count but no calculation (mean, median, interquartile
range etc.)
p-value (probability)
! if p-value low (<0.05), H0 must go (reject)
Conceptual Models
! Visual representations of relations between theoretical constructs (and variables) of interest
Moderation
One DV (Student satisfaction)
Two IVs (Commitment of teacher and communication skills)
!One variable moderates the relationship between two other variables
!When proposed effect is stronger in certain settings
!Moderation=Interaction
Mediation
A affects B and is affected by C
!When proposed relationship “goes via” another variable
! One variable mediates the relationship between two other variables
One-way ANOVA (Analysis Of Variance)
! Comparing groups (on quantitative variable, explained by PV/IV)
! How much of the variability of the independent variable is explained by the dependent variable
or
! Comparing the variability between the groups against the variability within the groups
Variance = the average of the squared differences from the mean (average)
Sum of Squares = the sum of the squared differences from the mean (average)
! Use of square in order to avoid negative values
,In Anova only one independent and one dependent variable:
- DV/OV has to be quantitative
- IV/PV has to be categorical with more than two groups
Pre Conditions / Assumptions:
- Variance is homogenous across groups (Leven’s Test)
! If not: Welch’s ANOVA
- Residuals are normally distributed
! If not: Kruskal-Wallis test
- Groups are roughly equally sized
- Subjects can only be in one group (between subjects design)
! If not: Repeated-measures ANOVA
1. Mean of all observations
2. Total sum squares
! General average (regardless groups)
3. Model sum of squares (Difference between the groups)
! Average of each group
! Difference is desired to be higher because (as difference between the group)
4. Residual (Differences within the groups)
! Square of the differences within a group
! Difference within the group is desired to be lower (as should be homogenous groups)
!Proportion of the total variance in data
, st
F-test (1 step)
! To investigate if the group means differ with an ANOVA
(Model/Residual)
Degrees of Freedom
! In order to find out ‘mean square’
!
Then compare value to f-table
Based on p-value reject or accept H0
EXAMPLE:
!Conclusion:
There is a statistically significant difference (p < .05)
between at least two of the groups
nd
Multiple Comparisons (2 step)
! To define which groups differ
- Statistically comparing each individual group’s scores against each one another
- Significance (alpha) at 0.05 (=5%), so Confidence level at 0.95 (=95%)
- P(Type I error) = 5%
- Multiple comparisons cause artificial inflation of alpha
- So we “adjust” for that. All post hoc tests are adjustments for this
- “Bonferroni” divides the alpha over all comparisons.
! 5 comparisons? Each gets 1%. So good if you have few comparisons
