Anova Flashcards
What are the statistical tests used to look for differences between a statistic from one sample and a population parameter?
z-test and one sample t-test
What type of test can be used when analyzing the mean of differences between two groups?
t-test
What test is used to find statistically significant differences between the means of two or more groups?
ANOVA
What does ANOVA use to draw conclusions about populations?
sample statistics
What is the independent variable called in an ANOVA?
factor
What does each factor in an ANOVA have that is represented by the variable k?
levels
In the study of human behavior under different lighting conditions, what is the dependent variable?
behavior
True or False: ANOVA can only be used for independent measures studies.
False
What is the null hypothesis (H0) in a one-way ANOVA involving three means?
μ1=μ2=μ3
What does the alternative hypothesis (Ha) state in a one-way ANOVA?
At least one of the means is different from the others
What is the F ratio in an ANOVA used to compare?
variance between samples and variance within samples
What is the formula for the F ratio?
F=VarianceBetweenSamples/VarianceWithinSamples
What type of ANOVA is used when testing the effect of one independent variable?
one-way ANOVA
What assumptions are made when using a one-way ANOVA?
population is normally distributed, samples have equal variances, samples are independent
What is the first step in hypothesis testing with one-way ANOVA?
State the Hypotheses
How is the degrees of freedom between (dfbn) calculated in a one-way ANOVA?
dfbn=k−1
How is the degrees of freedom within (dfwn) calculated?
dfwn=N−k
What is the critical value for a one-way ANOVA determined from?
F distribution table
What does a small F statistic (F<1) indicate about the variation within groups?
Variation within groups is greater than the variation between group means
What is the general format for reporting the results of a one-way ANOVA in APA format?
F(dfbn,dfwn)=F statistic, p-value
Fill in the blank: The null hypothesis (H0) states that all of the means being tested are _______.
equal
What increases the chances of a Type I error when performing multiple t-tests?
Performing multiple comparisons
What is the experiment-wise error rate?
Likelihood of a Type I error being made at some point throughout an experiment
What is the formula for calculating the sum of squares total (SStotal)?
SStotal=SSwn+SSbn
What does an ANOVA analyze to determine differences between group means?
Variance within and between groups
What does F(dfbn, dfwn) represent in statistics?
F statistic, p-value
What is the conclusion of the study if F(2,12)=1.58 and p>0.05?
There is not enough evidence to support the claim that the time of the statistics course affects exam performance
What does a small F statistic (F<1) indicate?
The variation within the groups is greater than the variation between group means
What does a large F statistic (F>1) indicate?
The variation between the group means is greater than the variation within the groups
What is the purpose of an ANOVA?
To determine whether there is evidence that a true difference exists between group means while taking the variance within each group into account
What are the components of an ANOVA table?
Degrees of freedom, Sum of Squares, Mean Squares, F statistic
What is the measure of effect size for a one-way ANOVA?
Eta squared (n2)
How is effect size (n2) calculated?
n2 = SSbn / SStotal
What does an effect size of n2=0.21 indicate?
It is large
What n2 values represent small, medium, and large effects?
- n2=0.01 (small)
- n2=0.06 (medium)
- n2=0.14 (large)
What is a post hoc test?
A test conducted after finding a statistically significant difference to identify where the differences lie
What is Tukey’s Honestly Significant Difference (HSD) test?
A common post hoc test used to compare mean differences between groups
What criterion is used for Tukey’s HSD test?
If the calculated mean difference is greater than the HSD value, there is a statistically significant difference
How is the HSD value calculated?
HSD = q * √(MSwn/n)
What does the q-value represent in Tukey’s HSD test?
The Studentized range statistic
What are the null and alternative hypotheses in a one-way ANOVA?
- H0: μ1=μ2=μ3 (no difference)
- Ha: At least one of the means is different
How do you calculate degrees of freedom between groups (dfbn) in a one-way ANOVA?
dfbn = k - 1
How do you calculate degrees of freedom within groups (dfwn) in a one-way ANOVA?
dfwn = N - k
What indicates a statistically significant result in ANOVA?
The calculated F-value exceeds the critical F-value
What is the effect size for the Flesch Reading Ease study?
n2=0.37
What does the conclusion state if the null hypothesis is rejected in the Flesch Reading Ease study?
There is evidence that a significant difference exists between the mean Flesch Reading Ease scores of the three books
What does ANOVA stand for?
analysis of variance
In an ANOVA, the independent variable is called a
factor
Each factor has a number of———-, represented by the variable k.
levels
The test statistic for an ANOVA is called the
F ratio
The likelihood of a Type I error being made at some point throughout an experiment is known as the
experiment-wise error rate
Since using multiple t-tests increases the experiment-wise error rate, an————- is an appropriate test to run when comparing three or more means.
ANOVA
A———— ANOVA is used when testing the effect of one independent variable, or factor.
one-way or one-factor
A one-way ANOVA assumes what 3 things?
-that the population is normally distributed
-the samples have equal variances
-the samples are independent
The F ratio measures differences between three or more group means by using the ratio of the variance between groups to the variance within groups. The value that is used to measure these variances is known as the
mean square (MS)
The results of an ANOVA are usually presented in an
ANOVA table
For a one-way ANOVA, the measure of effect size is known as
eta squared n2(the Greek letter eta squared)
When interpreting the n2 value, n2= ———- represents a small effect, n2= ———-represents a medium effect, and n2= ——-represents a large effect.
0.01
0.06
0.14
Another name for the effect size of an ANOVA result is the——————-.
proportion of variance accounted for
A common post hoc test is————-. It is a single value by which the mean difference between groups is compared.
Tukey’s Honestly Significant Difference (HSD) test
Note that the q-value for Tukey’s Honestly Significant Difference (HSD) test is called the———-
Studentized range statistic
In order to apply Tukey’s test, the groups must————.
be of equal size
