Factorial ANOVAs
What is it called when an interaction between two independent variables leads to the effect of one IV being strengthened by the level of another IV?
Quantitative - An interaction where the effect of one IV is strengthened or weakened by the level of another IV without directionality changing.
Using Cohen's conventions what is the strength of an r value of .30?
Moderate strength correlation
What is a multiple linear regression, and when would you use it?
Multiple Linear Regression - When you have 2+ predictor variables and 1 outcome variable
I want to determine only the relationship between how many apples I eat, and the number of doctor visits I have in a year.
What test should I consider running?
Pearson's Correlation
Come up with an example for a factorial ANOVA.
Any factor of IVs and their levels to determine a single DV.
ie time (week 1, week 2) vs infection status (infected, not infected) on changes in behavior; diet (high protein, low protein) vs. stress (high, low) on weight gain;
Say that I am studying the influence of drinking on math test results. I split my sample into four different groups for high alcohol or low alcohol intake the day before, and whether or not they took the math test in the morning or evening. This way I have two IVs, and want to compare means so I run a Factorial ANOVA.
If my partial eta-square value is 0.54 for alcohol intake, then how would you interpret this value?
About 54% variance in math test scores is explained by the alcohol intake the day prior.
This is a large effect size.
Come up with your own example of a correlational relationship with the intention of using Pearson's Correlation.
could be a comparison between any two typically continuous (ratio or interval) variables that are approximately normal;
ie ice creams bought vs drownings; number of ads seen vs self reported frustrations; heart rate vs time spent running; etc.
What is a Mean Center?
When you subtract a constant (mean) from every value of a variable to basically find the mean of the outcome variable.
Typically used when a scale does not contain a zero, so that the intercept can still be interpreted.
(ie the variable of weight cannot be a zero it doesn't make sense, so you use scaling/centering)
I want to predict how the value of a specific stock in the stock market based on the performance of that company.
What test should I consider running?
Binary Regression
What is the importance of standardizing the covariance between variables in correlations?
Hint: look at the r equation from the correlation powerpoint
Covariance shows and determines the direction of a correlation. It is calculated in the numerator of the r equation.
Covariance needs to be standardized because small and large sample sizes cannot be determined with the numerator alone. As such the denominator of the r equation the SD of both X and Y to "standardize" and determine strength and magnitude of correlations.
What do marginal means tell you?
Marginal means are the "margin" quantities showing the means within a single IV while accounting for other IVs.
Marginal means can be useful to see what direction a trend COULD be taking as well as a potential indicator of differences between groups even if not significant.
What is a partial correlation?
Method in which you statistically remove the influence of a third variable from two other variables
I am interested in looking at predicting national cheese consumption by ounce by the number of annual injury by being tangled in bedsheets. How do you interpret the R2 from the JASP table below?
Model Summary - Cheese Consumption (pounds)
Model R R² Adjusted R² RMSE
H₀ 0.000 0.000 0.000 1.202
H₁ 0.965 0.932 0.923 0.333
R2 = 0.923
Around 92.3% variance in cheese consumption is associated with changes in annual injury by bedsheets.
I want to compare the differences between-subjects in mean levels of reported frustration between swimmers and non-swimmers after being either hit by a water balloon or a paintball.
What test should I consider running?
Between-subjects Factorial ANOVA
When one variable is between-subjects and another is within-subjects.
Say, I am trying to study the optimal level of sunlight and water for my plant. So my independent variables are sunlight with high and low sunlight, and water quantity with high and low water. My dependent variable is plant growth in centimeters. I collect information, and run a Factorial ANOVA.
Using this example, what would be the main effects and what would be an interaction?
2 Main Effects - Sunlight + Water on Plant Growth
1 Interaction - Sunlight x Water interact to influence Plant Growth
What correlation do you use if one of your variables is nominal?
When using a multiple regression, how do you determine which variable is the better predictor?
Use the standardized values of each. The larger standardized variable is the indicator for that variable being a better predictor.
I want to compare a the top students (my sample) to the rest of the school (population of interest) on levels of self reported stress, but I don't have the standard deviation of the school.
What test should I consider running?
One Sample t-test
What is the other name for R2?
The coefficient of determination
A study was done measuring heart rate based on gender and whether the participant was a runner or not.
Read this JASP table below. Are there any main effects? Are there any interactions? How strong is the effect size for each?
Cases SS df MS F p η²
Gender 45030 1 45030 185.98 .001 0.110
Group 168432 1 168432 695.647 .001 0.413
G✻G 1794 1 1794 7.409 .007 0.004
Main Effect of Gender with a η² = 0.110, meaning 11% variance in heart rate can be attributed to gender.
Main Effect of Group with a η² = 0.413, meaning 41.3% variance in heart rate can be attributed to group.
Interaction Effect of Gender and Group with a η² = 0.004, meaning 0.4% variance in heart rate can be attributed to the interaction of gender and group
I want to see what the correlation is between the price an auction item is sold for and the number of bidders for that item. Please interpret this table below. What type of relationship is this, what is its strength and is it significant?
Price Bidders Price
Pearson's r 0.395 —
p-value .025 —
A Pearson bivariate correlation reveals a significant, moderate strength, positive relationship between the price of the item and the number of bidders, r = 0.395, p = .025.
What would be the linear equation y = a + b1x1 from this JASP table below?
H₀ (Intercept) 31.630
(Undstandardized) 0.380
(p-value) < .001
H₁ (Intercept) 27.655
(Unstandardized) 0.006
(Standardized) 0.965
(p-value) < 0.001
y = 27.66 + 0.006x
I want to compare the differences in mean in guilt verdicts from scale of 0-100 in participants reading a court trial both over time comparing the first week and second week verdicts, between participants who have just eaten lunch and participants who have not eaten lunch.
What test should I consider running?
Repeated Measures Factorial ANOVA
For instance, how many IVs are there and how many levels do they have in a 2x2x3 Factorial ANOVA?
3 IVs in total, two have 2 levels and one has 3 levels