Ch. 14: Two-Way ANOVA
This is the name and definition of the effect size statistic for two-way ANOVA.
What is R2 (percent variance explained by factor)?
I design a correlational study on exercise and sleep habits in older adults. I recruit 45 subjects to take part, but 4 subjects drop out. This is my degrees of freedom for the study
What is 39? ((45 - 4) - 2)
This is the equation for degrees of freedom for a Χ2 test for goodness of fit.
What is dfΧ2 = k - 1? (Where k is the number of categories)
A researcher is examining the relationship between bee species and pollination patterns. They record amount of pollen delivered by 20 honeybees and 20 bumblebees over the course of several days. This statistical test is appropriate.
What is an independent-samples t test? (2 groups, 1 scale variable)
This is the most significant difference between reporting the results of a one-way ANOVA and reporting the results of a two-way ANOVA.
What is the presentation of three F tests (one for rows, one for columns, and one for the interaction effect)?
A researcher reports a correlation of 0.41 in a study with 16 subjects. The researchers report the results as significant: r(16) = 0.41, p < 0.05. Spot and correct at least one mistake in their reporting.
What is incorrect degrees of freedom? With 16 subjects we have 16-2 = 14 degrees of freedom; examining the Pearson's r critical table we see a p < .05 critical threshold of r=0.426 for 14 degrees of freedom. The result is not significant!
This is the class of statistics that the Χ2 test belongs to.
What are non-parametric statistics?
A researcher wants to examine the relationship beween shoe size and basketball ability. They record the shoe size and number of free throws made out of 100 from 1500 basketball players. This statistical test is appropriate.
What is regression/correlation?
This is the equation for determining the sum of squares of the interaction effect (SSinteraction) in terms of the total, row-wise, column-wise, and within-group sum of squares (SSTotal, SSrow, SScolumn, and SSwithin)
What is:
SSinteraction = SSTotal - (SSrow + SScolumn + SSwithin) ?
A study examining the relationship between how long you sleep and how recently before going to bed you have eaten finds a significant correlation between # of hours slept and # of hours before bed one has eaten.
SPSS reports the regression line y = α + Βx (where y is # hours slept and x is # hours before bed the subject had eaten) as α = 6 and Β = -1.5. Interpret the regression line. :)
What is:
People who ate right before bed (x = 0) slept the longest (α = 6 hours). The longer it had been since eating, the worse participants slept (negative Β). I.e. people who ate 1 hour before (on average) only slept 4.5 hours; ate 2 hours before => 3 hours slept etc.
This is the effect size for a Χ2 test.
What is Cramér's V?
What is the Χ2 test for goodness of fit?
A study surveying 120 young students (10 per group) reports a significant main effect of hair color (brown, blonde, or other) in study habits following one of four cognitive training methods: F(2,3) = 17.1, p < 0.05. Spot and correct the mistake the researchers made in reporting their results.
What is incorrect degrees of freedom? Here, hair color is our independent variable, and study habits in each of 4 subjects is our dependent variable. So, the study should report the between-hair-color-group degrees of freedom (3 hair groups - 1 = 2and the within-groups degrees of freedom (12 groups * (10 subjects per group - 1) = 108). The researchers should also present the results of the main effect of experimental treatment as well as any interaction effects.
This is a description of the regression to the mean statistical phenomenon.
What is that multiple observations/generations of extreme values have a tendency to become less extreme over time?
This is the major difference between the Χ2 test for goodness of fit and the X2 test for independence.
What is goodness of fit tests whether a single nominal variable differs between groups, whereas a independence test examines whether two nominal variables are independent of each other?
I have data from 1000 teens including Myers-Briggs personality type information (16 personality types; each subject is a combination of extrovert vs. introvert, intuitive vs sensing, thinking vs feeling, and judging vs. perceiving). I suspect there are differences in study habits between extroverted/introverted subjects, and between thinking/feeling subjects. This statistical test is appropriate.
What is planned comparisons?
Complete the table:
Source | SS | df | MS | F |
_______________________________
Rows | 40 | 2 | ? | 10
Cols | 24 | ? | 8 | ?
Int | ? | 6 | 2 | ?
Within | ? | ? | ? |
Total | 110 | 27 |
Hint: Need to find MSwithin to find the F values
What is:
MSrows = SSrows / dfrows = 40/2 = 20
dfcols = SScols / MScols ...
= dfint / dfrows
= 24/3 = 8 ...
SSint = MSint * dfint = 2 * 6 = 12
SSwithin = SStotal - (SSrows + SScols + SSint) ... = 108 - (40 + 24 + 12) = 32
dfwithin = dftotal - (dfrows + dfcols + dfint) ...
= 24 - (2 + 3 + 6) = 16
MSwithin = MSrows/Frows = 20/10 = 2
Fcols = MScols / MSwithin = 8 / 2 = 4
Fint = MSint / MSwithin = 2 / 2 = 1
Helpful equations:
F = MSfactor / MSWithin
MSfactor = SSFactor / df
SStotal = SSrows + SScols + SSint + SSwithin
dfinteration = (dfrows)*(dfcols)
dftotal = dfrows + dfcols + dfint + dfwithin
dfwithin = sum(dfcells) = sum(nsubjects_per_cell-1)
I have four data points: (1,14), (1.5, 12), (2.5, 8), (3,6). This is the correlation coefficient.
What is -1?
Suppose I have a Χ2 test of independence on two factors, one with 3 levels and the other with 4 levels. I find a test statistic of 16.9. This is the highest p-value threshold at which this test significant.
What is α = 0.01? (Degrees of freedom = (nrows-1)*(ncols-1) = 3*2 = 6)
A researcher wants to examine differences in luminance perception by eye color (blue, brown, green). They design and run a training aiming to improve performance in a luminance change detection task. This statistical test is appropriate.
What is one-way repeated measures (or within-group) ANOVA?