Samenvatting
Summary ARMS - overview of all statistical analyses including steps and key points.
An overview of all analyses covered in the ARMS course at the UU, the 3/3 statistics course in the bachelor psychologie.
[Meer zien]Voorbeeld 2 van de 5 pagina's
Voorbeeld 2 van de 5 pagina's
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Voorbeeld van de inhoud
Initial assumptions1. DV is continuous: interval or ratio
2. IV’s are continuous or
dichotomous (nominal with two
Multiple Linear Regression (MLR)
categories) Book summary
3. There is a linear relationship
SSR = Goodness of fit (small is good)
between all IV’s and the DV (an
oval shaped scatterplot) OLS = ordinary least squares = finds
4. There are no outliers the b-value with the least residuals. Interpreting
SST= how good is the mean as a model R = multiple correlation coefficient = Basic equation
Statistical assumptions for observed scores = difference correlation of Y and ŷ = how good is
between observed values and model = the prediction of Y. Yi = B0 + B1X1i + B2X2i + B3X3i + ei
1. Absence of outliers: Σ (y - 𝑦̅)2
- On X: Mahalanobis distance is
R2 x 100 = variance explained
< 10 + 2*amount of IV’s SSM = differences between the mean Comparing models by pressing next Dummy coding
- On Y: standardized residuals and model = Σ (ŷ - 𝑦̅)2 after adding each variables, will Dummy variables need to be
are not < - 3.3 or > 3.3 give you change statistics. dichotomous (2 categories).
SSR = differences between observed
- On XY: Cook’s distance < 1 R2 change = amount of variance
values and the model = Σ (y - ŷ)2 Steps:
- If theoretically possible explained extra compared to
compare analysis with and 1. Number of groups – 1
R2 = SSM/SST previous model (check sig. F
without the subject. 2. Create this number of variables
𝑒𝑥𝑝𝑙𝑎𝑖𝑛𝑒𝑑 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑀𝑆𝑀 change). 3. Choose your reference group
2. Absence of multicollinearity: F = 𝑢𝑛𝑒𝑥𝑝𝑙𝑎𝑖𝑛𝑒𝑑 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝑀𝑆𝑅 ANOVA F-test is different and (which is most relevant?)
- Coefficients table: tolerance
values < .2 are potential Good = MSM is large and MSR is small calculated per model. 4. Give reference group a value
problems. <.1 is a problem. of 0 on all variables
SS .. → MS .. = SS/df 5. Give the other groups a value
- VIF > 10 = problem Extra
- VIF = 1/tolerance MSM = SSM/k & MSR = SSR/N-k-1 of 1 for their variable
Generalisability: adjusted R2 or use 6. Change dummy names to
- Relationship > .8 is too strong data splitting (are halves very different)
- In case of multicollinearity: N = number of observations which comparison it is
unreliable B’s, limitations of R K = number of predictors/IV’s Flat model = regression coefficient Procedure:
and no importance of B1 = 0
- Transform → recode into
individual variables is known F is also used to test the null hypothesis
Assumptions not met? Use bootstrap or different variables.
3. Homoscedasticity: see plot of R2 = 0. robust regression. - Old → new name and change
4. Normally distributed residuals: see t-test = null hypothesis that B1 = 0 → - Group ,, → 1
plot Eigenvalue > 1 will be included.
- System/user missing → system
- Plot: ZRESID = Y & ZPRED = 𝑏𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 − 𝑏𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 Casewise diagnostics: cases that need missing
X 𝑆𝐸𝑏 extra attention due to values. - All other values → 0
, -----------------------------------------------------------------------------------------------------
In SPSS
Moderation
PROCESS tool is needed
Simple slope analysis: looking at the
Moderation
effect of the moderator at different
Moderation = a moderator affects the levels (low, mean, high).
direct effect of X on Y, in strength or
Zone of significance: when looking at a
direction.
lot of values for the moderator, two Mediation
values will be most significant. The in
between bit isn’t as much influenced by Mediator: the relationship between x
the moderator. and y can be explained by this variable.
When interaction effect is significant
make a grouped scatter plot where Xi
on the x-axis and Yi on the y-axis. Put
Effects of a moderator can depend on
the moderator on set colour.
the value of that variable or be
categorial. → Check if the effect between groups Mediation
is different.
Equation: (M being the moderator) c = normal effect of X on Y.
PROCESS (model 1): In SPSS
ŷ = b0 + b1X1i + b2Mi + b3X1iMi With analyses you want to get the b-
- Options: choose generate code, values for a, b, c and c’. Use PROCESS + choose model 4
You will be testing three effects: main
mean center, p < .05 & -/+ 1 SD.
effect of X, main effect of M and Via linear models you test the Choose effect size and total effect
- What does the relationship look
interaction of X*M. significance of these effects. boxes.
like? Write out regression
B1 = effect on Y when other b’s are 0. equations, check conditional Complete mediation when c’ = 0. Output per table:
effects or visualise (put the part of
- Theoretically can be impossible. ‘data list free/’ in new syntax) Effect sizes of mediation: 1. Effect a
- Interaction variable makes it hard - Johnson-Neyman method when the 2. Effect c’ and b
to look at the other effects - Indirect effect = a*b
moderator is continuous (zone of 3. Path c (total effect model)
separately. So you centre your - Partially standardized indirect
significance). Check this box! 𝑎∗𝑏 4. All effects
variables to z-scores (= Grand effect = 𝑆𝐷𝑜𝑢𝑡𝑐𝑜𝑚𝑒
mean centering). If you have 1 categorical variable, a - Fully standardized = index of Completely standardized indirect effect
- B2 = what is the effect of b1 on Y value of 0 on that will make the mediation = when X is dichotomous.
for an average score on b2. interaction 0. If you have 2 continuous 𝑎∗𝑏
𝑥 𝑆𝐷𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑜𝑟 Partially standardized indirect effect
→ This makes low-order b’s variables the interaction scores will 𝑆𝐷𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑎∗𝑏 𝑎∗𝑏 when you want to compare effects
interpretable. differ more. - Can be estimated by 𝑜𝑟
𝑐 𝑐′ across studies.
Use a difference variable (follow-pre) - Standard error = the SD for sample
Order = higher the more variables you
when looking at improvement. means in a distribution. Use bootstrap → look at CI’s for sig.
have, less influence on centering.
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