module 11 Flashcards
f-test
- used to evaluate difference in variable between groups
- Fo=s2a/s2b
- observed variance= data1/data2
t or f for f tests,
dfA: degrees of freedom for group A is dfA=nA-1 where nA is the number of sampling units in group A.
true
how decimal points do you report your p value to when doing a scientific conclusion
3
the f test is used to evaluate whether the variances of _______ are different
two group
what is ANOVA also known as
analysis of variance
what is an ANOVA
method to work with data that has both numerical and categorical variables
when to use ANOVA vs two sample t test
t test: two levels in a categorical variable
ANOVA: more than two levels
ANOVA test works be separating data into two sources of variation: _____ and ______
- group variation (variation among categorical levels)
- residual variation (variation within a categorical level ie within sampling units)
If the means of two groups are the same, then the variation among the groups is ______
0
If the means among the groups are quite different, then the variation among the groups is ______
high
t or f: the variation among the groups is a direct indicator as to whether the groups have different means
true
ANOVA models evaluate _____________ among the categorical levels
whether there is a difference in the means
the stats model for ANOVA looks at the ratio of the _______ over the _______
group variation, residual difference
If the group variation is about the same size as the residual variation, then the means of the levels are _____________
not overly different
If the group variation is much larger than the residual variation, then the groups are _______
different
Since ANOVA uses a ratio of variances (group/residual), the statistical model boils down to ________
an F-test
what questions are two factor ANOVAs used for
- main effects A (differences among levels of factor A averaging across levels of factor B, compare among full columns/rows)
- main effects B (differences among levels of factor B averaging across levels of factor A, compare among full columns/rows)
- interactions (questions abt differences among levels of one factor within each level of other factors. cell-by cell comparison)
additivity
the response to the combination of two levels is simply the sum of the two
(ie two 1 pound weights is two pounds)
What is group variation?
The variation between the group means and the overall grand mean.
What is residual variation?
The variation between the sampling units and the group means.
To calculate the f-score you:
The F-score = group variation divided by residual variation.
interaction is defined as any deviation from ______
additivity
The null and alternative hypothesis are directional because
Since our interest is in whether the means are different, we are evaluating whether the group variation is larger than the residual variation. As such, the null and alternative hypotheses are directional. HO: F≤1 HA: F>1
how are interaction plots set up
- y-axis shows numerical variable (like box plot)
- x-axis shows levels one categorical variable
- lines connect cells across x axis according to levels of other categorical variables
dfG vs dfG
dfG: degrees of freedom for the group variation is dfG=k-1 where k is the number of levels in the categorical variable.
dfE: degrees of freedom for the residual variation is dfE=n-k where n is the total number of sampling units in the dataset and k is the number of levels in the categorical variable.
if the categorical variables are additive they have ______ interaction
no, parallel lines on an interaction plot
Statistical decisions for f-score tests (for the hypothesis)
- Reject the null hypothesis if the observed score is greater than the critical score (i.e., FO>FC) or if the p-value is smaller than the Type I error rate (i.e., p<⍺).
- Fail to reject the null hypothesis if the observed score is less than or equal to the critical score (i.e., FO≤FC) or if the p-value is larger or equal to the Type I error rate (i.e., p≥⍺).
t or f: if two categorical variables are not additive (ie they have an interaction) the lines on an interaction plot are parallel
false
The scientific conclusions for an ANOVA are:
- Reject the null hypothesis and conclude there is evidence that at least two of the means are different.
- Fail to reject the null hypothesis and conclude there is no evidence that the means are different.
main A effects null and alt hypotheses for a two factor ANOVA:
a) Ho: μA1=μA2=…=μAk-1=μAk and Ha: μA1≠μA2≠…≠μAk-1≠μAk
b) Ho: μB1=μB2=…=μBk-1=μBk and Ha: μB1≠μB2≠…≠μBk-1≠μBk
c) Ho: δA1B1=δA1B2=…=δAkBk-1=δAkBk=0 and Ha: δA1B1≠δA1B2≠…≠δAkBk-1≠δAkBk≠0
a)
Reporting of an ANOVA should include the following:
- The mean, standard deviation, and sample size for each group (ideally in a table)
- The observed F-score (two decimal places)
- degrees of freedom for the group variation and the residual variation
- p-value (three decimal places)
Rejecting the __(1)__ hypothesis of the ___(2)___ means that at least two of the groups are different. The __(2)__cannot identify how many groups are different, nor identify which ones.
- Null
- F-test
TukeyHSD test
A type of post hoc test that evaluates all possible contrast statements
main B effects null and alt hypotheses for a two factor ANOVA:
a) Ho: μB1=μB2=…=μBk-1=μBk and Ha: μB1≠μB2≠…≠μBk-1≠μBk
b) Ho: μA1=μA2=…=μAk-1=μAk and Ha: μA1≠μA2≠…≠μAk-1≠μAk
c) Ho: δA1B1=δA1B2=…=δAkBk-1=δAkBk=0 and Ha: δA1B1≠δA1B2≠…≠δAkBk-1≠δAkBk≠0
a)
main B effects null and alt hypotheses for a two factor ANOVA:
a) Ho: μB1=μB2=…=μBk-1=μBk and Ha: μB1≠μB2≠…≠μBk-1≠μBk
b) Ho: δA1B1=δA1B2=…=δAkBk-1=δAkBk=0 and Ha: δA1B1≠δA1B2≠…≠δAkBk-1≠δAkBk≠0
c) Ho: μA1=μA2=…=μAk-1=μAk and Ha: μA1≠μA2≠…≠μAk-1≠μAk
b)
Post hoc tests
Secondary tests uses to evaluate what groups have diffferent means in an ANOVA. The role of a post hoc test is to evaluate whether group means are different while controlling for the Type I error rate for all comparisons among groups.
When are you able to use post hoc tests?
They are only used if the ANOVA F-test indicates to reject the null hypothesis.
What is the purpose of a contrast statement
To test the difference in means between two groups in an ANOVA
Family of contrasts
The set of all contrast statements used for a set of data
Family-wise error rate
The Type I error rate for the family of contrasts
Contrasts
A test of the difference in means between two groups in an ANOVA
If the _____________ is not controlled, increasing the number of contrast statements quickly increases the effective Type I error.
- family-wise error rate
_________ is one type of post hoc test that compares the means of all possible contrasts. It uses a specialized null distribution to adjust for the number of contrasts.
- TukeyHSD
