Tutorial SUMMARY
Tutorial 1 AN(CO)VA
Problem 1A
1. Which assumptions are made in multiway ANOVA?
• The residu ij should be normally distributed within each cell of the design
• The residu ij should have the same variance within each cell of the design
(homoscedasticity)
• The factors are fixed and without measurement error
Conclusions can only be drawn for the selected levels;
Interpolation may be possible, extrapolation is forbidden;
o Measurement error → underestimation of the strength of the effect
• The observations on the dependent variable should be independent (you can’t use F
when data is dependent )→ correction for the F is the Bonferoni test.
• The dependent variable should be of at least interval scale level → levine test,
because it is not based on the normality assumption.
• State the null and alternative hypotheses
• Collect the data and provide a summary
• Choose a level of uncertainty
• Compute the test statistic
• Take a decision
• Draw a conclusion
2. What is confounding?
An variable that distord the effect of the dependent and the independent variable.
3. Explain why multiway ANOVA may be useful in the case of potential
confounders.
If you want to see the interaction between more then 2 variables.
4. What is the difference between confounding and effect modification?
Effectmodificator shows that there is an interaction.
5. Explain why it is not useful to inspect main effects when there is a significant
interaction effect (involving the same factors as involved in the main effects).
the mean stays the same
Which analysis should be done after a significant interaction is found?
you need make two conclusions→ just separet the two groups
6. Why is it useful to extend the analysis of variance to the analysis of covariance?
Anova → ancova when there are continues factors involved. You adjust for a
continues variable (ratio or interval).
,7. Which additional assumptions are made in analysis of covariance?
• Linearity of the relation between the covariate and the dependent variable;
make for each group a scatterplot of the covariate versus the dependent variable.
• Classic ANCOVA: no interaction between the factor and the covariate;
calculate a new variable:
interact = stress x age
Include this variable as an extra covariate in the analysis of covariance
• The residu i(j) should be normally distributed within each cell of the design with the
same variance
• The covariates (and factors) are fixed and without measurement errors:
o sample results can only be generalized to populations where the covariates
have the same values (interpolation may be possible)
o measurement error attenuates the strength of relations
Remedy for measurement error:
Measure the covariate multiple times and take the average value
• The observations on the dependent variable should be independent
• The dependent variable should be of at least interval scale level
8. Explain how one can test for these specific assumptions.
Linearity make a scatter pollt → dependent vs the covariant
There should be lineauroty in each cell, between the dependent and the covariant
9. What is an unbalanced design?
Different amout of partispants in the groups
, 10. Give several implications in the case of (co)variance analysis when we have an
unbalanced design. Discuss the statistical testing of interactions and the method
for conducting the analysis of (co)variance.
Type 3 of sum of squire
So there are different types of sum of squire
Problem 2A
1. Examine analysis A and explain which analysis has been performed here. Which
analysis has been performed in analysis B? Explain whether analysis A improves
analysis B in terms of power or correction for confounding.
Analysis a → age (continues) and smoking (catogorie) analyses of covariance → ancova
Analysis B→ you have just one variable→ one way anova
Analysis improves a -b, mean squire error gets less → power increases when using one-way
anova.
Age was confounding it.
Age is correlated with smoking and bloodpressure (71.763 ) smoking and age (-.139. Pvalue
is very high so there is no correlation.
2. Explain whether there is an effect of smoking and explain how large this effect is.
Analysis b smoking increases bloodpressure by 10.294
3. Which assumptions can be assessed in analysis C and D. Are these assumptions
satisfied?
C → linearity smokers and not smokers
D→ smok x age → 0.292 no sig interaction (unbalanced) → shows effectmodifaction.
Make a new model→ analysis a
For increase of one year in age the bloodpressure increases 1.709
-10,2994 we assume age is fixed.
, AN(CO)VA: tutorial 2 (A3-A6)
Problem A3
Formulate the 2 main research questions and discuss how you will answer them. Write
the statistical procedure section of the statistical analysis plan, that is, describe all the
steps that will be performed in your statistical analysis to answer the research questions.
Research Q1: What is the role of drinking water nitrate exposure as a risk factor for gastric cancer
incidence in Mid-Atlantic region
Research Q2: is smoking an effect modifier between nitrate levels in drinking water and the
incidence of gastric cancer
Drinking water: 3 groups
“low” risk group exposed to 0.13mg/L,
“medium” risk group exposed to 32.0mg/L
“high” risk group exposed between 56 and 311 Mg/L
Natrium intake: 3 groups
total nitrate intake in mg per day through food (NO3FOOD),
through water (NO3WATER)
the total nitrate excretion in mg per day through urine (NO3URIN).
State the null and alternative hypotheses
H0= there is no relation/interaction between nitrate in drinking water and chromosome
defects in the lymphocytes.
Ha= there is an relation/interaction between nitrate in drinking water and chromosome
defects in the lymphocytes.
Collect the data and provide a summary
Choose a level of uncertainty
Tutorial 1 AN(CO)VA
Problem 1A
1. Which assumptions are made in multiway ANOVA?
• The residu ij should be normally distributed within each cell of the design
• The residu ij should have the same variance within each cell of the design
(homoscedasticity)
• The factors are fixed and without measurement error
Conclusions can only be drawn for the selected levels;
Interpolation may be possible, extrapolation is forbidden;
o Measurement error → underestimation of the strength of the effect
• The observations on the dependent variable should be independent (you can’t use F
when data is dependent )→ correction for the F is the Bonferoni test.
• The dependent variable should be of at least interval scale level → levine test,
because it is not based on the normality assumption.
• State the null and alternative hypotheses
• Collect the data and provide a summary
• Choose a level of uncertainty
• Compute the test statistic
• Take a decision
• Draw a conclusion
2. What is confounding?
An variable that distord the effect of the dependent and the independent variable.
3. Explain why multiway ANOVA may be useful in the case of potential
confounders.
If you want to see the interaction between more then 2 variables.
4. What is the difference between confounding and effect modification?
Effectmodificator shows that there is an interaction.
5. Explain why it is not useful to inspect main effects when there is a significant
interaction effect (involving the same factors as involved in the main effects).
the mean stays the same
Which analysis should be done after a significant interaction is found?
you need make two conclusions→ just separet the two groups
6. Why is it useful to extend the analysis of variance to the analysis of covariance?
Anova → ancova when there are continues factors involved. You adjust for a
continues variable (ratio or interval).
,7. Which additional assumptions are made in analysis of covariance?
• Linearity of the relation between the covariate and the dependent variable;
make for each group a scatterplot of the covariate versus the dependent variable.
• Classic ANCOVA: no interaction between the factor and the covariate;
calculate a new variable:
interact = stress x age
Include this variable as an extra covariate in the analysis of covariance
• The residu i(j) should be normally distributed within each cell of the design with the
same variance
• The covariates (and factors) are fixed and without measurement errors:
o sample results can only be generalized to populations where the covariates
have the same values (interpolation may be possible)
o measurement error attenuates the strength of relations
Remedy for measurement error:
Measure the covariate multiple times and take the average value
• The observations on the dependent variable should be independent
• The dependent variable should be of at least interval scale level
8. Explain how one can test for these specific assumptions.
Linearity make a scatter pollt → dependent vs the covariant
There should be lineauroty in each cell, between the dependent and the covariant
9. What is an unbalanced design?
Different amout of partispants in the groups
, 10. Give several implications in the case of (co)variance analysis when we have an
unbalanced design. Discuss the statistical testing of interactions and the method
for conducting the analysis of (co)variance.
Type 3 of sum of squire
So there are different types of sum of squire
Problem 2A
1. Examine analysis A and explain which analysis has been performed here. Which
analysis has been performed in analysis B? Explain whether analysis A improves
analysis B in terms of power or correction for confounding.
Analysis a → age (continues) and smoking (catogorie) analyses of covariance → ancova
Analysis B→ you have just one variable→ one way anova
Analysis improves a -b, mean squire error gets less → power increases when using one-way
anova.
Age was confounding it.
Age is correlated with smoking and bloodpressure (71.763 ) smoking and age (-.139. Pvalue
is very high so there is no correlation.
2. Explain whether there is an effect of smoking and explain how large this effect is.
Analysis b smoking increases bloodpressure by 10.294
3. Which assumptions can be assessed in analysis C and D. Are these assumptions
satisfied?
C → linearity smokers and not smokers
D→ smok x age → 0.292 no sig interaction (unbalanced) → shows effectmodifaction.
Make a new model→ analysis a
For increase of one year in age the bloodpressure increases 1.709
-10,2994 we assume age is fixed.
, AN(CO)VA: tutorial 2 (A3-A6)
Problem A3
Formulate the 2 main research questions and discuss how you will answer them. Write
the statistical procedure section of the statistical analysis plan, that is, describe all the
steps that will be performed in your statistical analysis to answer the research questions.
Research Q1: What is the role of drinking water nitrate exposure as a risk factor for gastric cancer
incidence in Mid-Atlantic region
Research Q2: is smoking an effect modifier between nitrate levels in drinking water and the
incidence of gastric cancer
Drinking water: 3 groups
“low” risk group exposed to 0.13mg/L,
“medium” risk group exposed to 32.0mg/L
“high” risk group exposed between 56 and 311 Mg/L
Natrium intake: 3 groups
total nitrate intake in mg per day through food (NO3FOOD),
through water (NO3WATER)
the total nitrate excretion in mg per day through urine (NO3URIN).
State the null and alternative hypotheses
H0= there is no relation/interaction between nitrate in drinking water and chromosome
defects in the lymphocytes.
Ha= there is an relation/interaction between nitrate in drinking water and chromosome
defects in the lymphocytes.
Collect the data and provide a summary
Choose a level of uncertainty
