Definitions
A combination of levels from different factors.
What is a Treatment?
Two diets are compared to see which is more effective.
This method would be used for inference.
What is a two-sample t-test or One-Way ANOVA?
We wish to compare three different teaching methods/class types on their impact on student learning. We first measure each student's knowledge before taking the course (PRE test score) as it would affect their learning. Each student is randomly assigned to take one of the class types and given a standardized test at the end of the course (POST test score).
trig.model <- lm(POST ~ CLASSTYPE + PRE)
summary(trig.model)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.372 1.810 5.73 5.1e-07
CLASSTYPE2 -0.957 1.582 -0.60 0.548
CLASSTYPE3 4.058 1.632 2.49 0.016
PRE 0.773 0.170 4.54 3.4e-05
When comparing students who had the same pre-test score, students who took ClassType 3 scored on average these many more marks than those in ClassType 1.
What is 4.058?
This means we keep the variable constant for all treatment conditions.
What is Control?
A categorical variable that is manipulated by the experimenter.
What is a Factor?
We wish to compare three different teaching methods on their impact on student learning. Each student is randomly assigned to take one of the teaching methods and given a standardized test at the end of the course.
This method should be used for this scenario.
What is One-Way ANOVA?
We wish to compare three different teaching methods/class types on their impact on student learning. We first measure each student's knowledge before taking the course (PRE test score) as it would affect their learning. Each student is randomly assigned to take one of the class types and given a standardized test at the end of the course (POST test score).
trig.model <- lm(POST ~ CLASSTYPE + PRE)
summary(trig.model)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.372 1.810 5.73 5.1e-07
CLASSTYPE2 -0.957 1.582 -0.60 0.548
CLASSTYPE3 4.058 1.632 2.49 0.016
PRE 0.773 0.170 4.54 3.4e-05
This is the average score for all students who took ClassType 1 and got 0 on the pre test.
What is 10.372?
This is done to spread out variables evenly across all treatments and minimize the chance of confounding.
What is Randomization?
An experiment in which every experimental unit is given every treatment.
What is a Within-Subjects design?
We wish to compare three different teaching methods on their impact on student learning. Each student is randomly assigned to take one of the teaching methods and given a standardized test at the end of the course. We also measure each student's IQ as it would affect their learning.
This method should be used for this scenario.
What is ANCOVA?
We wish to compare three different teaching methods/class types on their impact on student learning. We first measure each student's knowledge before taking the course (PRE test score) as it would affect their learning. Each student is randomly assigned to take one of the class types and given a standardized test at the end of the course (POST test score).
trig.model <- lm(POST ~ CLASSTYPE + PRE)
summary(trig.model)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.372 1.810 5.73 5.1e-07
CLASSTYPE2 -0.957 1.582 -0.60 0.548
CLASSTYPE3 4.058 1.632 2.49 0.016
PRE 0.773 0.170 4.54 3.4e-05
When comparing students in the same class type, a one mark increase in the pre test score, on average, increases the post test score by these many marks.
What is 0.773?
In this principle, we assign more than one experimental unit to each treatment to ensure the result is not due to the experimental unit.
What is Replication?
The effect of one factor on the response changes according to the level of the other factor.
What is Interaction?
Nine dish washing soaps are to be compared and we have 3 washing basins (with one dish washer for each basin) available. Each dish washer washes at the same speed but speed might vary between washing sessions. The experiment will be conducted with 12 sessions.
This type of design should be used.
What is a BIBD?
We wish to compare three different teaching methods/class types on their impact on student learning. We first measure each student's knowledge before taking the course (PRE test score) as it would affect their learning. Each student is randomly assigned to take one of the class types and given a standardized test at the end of the course (POST test score).
trig.model <- lm(POST ~ CLASSTYPE + PRE)
summary(trig.model)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.372 1.810 5.73 5.1e-07
CLASSTYPE2 -0.957 1.582 -0.60 0.548
CLASSTYPE3 4.058 1.632 2.49 0.016
PRE 0.773 0.170 4.54 3.4e-05
This is the p-value for testing:
"When comparing students that scored the same on the pre test, Class Type 2 is different than Class Type 1."
What is 0.548?
A covariate that is categorical.
What is a Blocking Variable?
This is a design in which all combinations of the factor levels have at least one experimental unit.
What is Complete?
A study is conducted using 10 people to determine which of two types of insect repellent is more effective. For each person, one arm is randomly selected to receive the first type of insect repellent while the second type of repellent is applied to the other arm. After 5 hours, the number of insect bites is counted on each arm.
This method should be used for this scenario.
What is a RCB design or paired/matched t-test?
We wish to compare three different teaching methods/class types on their impact on student learning. We first measure each student's knowledge before taking the course (PRE test score) as it would affect their learning. Each student is randomly assigned to take one of the class types and given a standardized test at the end of the course (POST test score).
trig.model <- lm(POST ~ CLASSTYPE + PRE)
summary(trig.model)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.372 1.810 5.73 5.1e-07
CLASSTYPE2 -0.957 1.582 -0.60 0.548
CLASSTYPE3 4.058 1.632 2.49 0.016
PRE 0.773 0.170 4.54 3.4e-05
This is the p-value for testing:
"When comparing students that scored the same on the pre test, Class Type 3 scores on average higher than Class Type 1."
What is 0.008?
https://www.youtube.com/watch?v=Yx6UgfQreYY
This principle was definitely not used in this experiment.
What is Replication?