One sample analysis of variance (Anova)
What is unique/ different about a one way within subjects ANOVA?
A one way within subjects ANOVA has an additional variance which is removed before calculating the test statistic.
What is a post hoc test and what is its purpose?
A post hoc test is a statistical procedure computed following a significant ANOVA to determine which pair or pairs of group means significantly differ.
What does the post hoc test evaluate?
A post hoc tests evaluates the differences for all possible pairs of group means, called pairwise comparisons
For stage 1: preliminary calculations, what are the three summations we must find?
Preliminary calculation requires that we find summation Xt , summation x^2, summation X^2T
How many sources of variation are present in a one way b/w subjects anova?
There are two sources of variation in a one way b/w subjects anova?
What does one way ANOVA indicate?
A one way Anova indicates that we are testing one factor.
What are other terms that can be used to describe "variance b/w groups" and "variance within groups"
"Variance b/w groups" can be described by the phrase mean square b/w groups "variance within groups" can be described by the phrase mean square error
Find summationX and summation Xt
2 1 4 2 5 4 6 6 X=17, x=13 summation xt= 30
How many calculations are required in stage 2 of intermediate calculations?
3 calculations - (1), (2), (3)
How many steps are required to find turkeys HSD? What are the steps?
3 steps are required to find turkeys HSD The three steps 1. compute each test statistic for each pair wise comparison 2. compute the critical value for each pairwise comparison 3. make a decision to retain to reject the null of each pairwise comparison
What is a b/w persons variation?
A b/w persons variation is unique to one way within subjects anova and is attributed to observing the same participant in each group
What is an ANOVA test?
A statistical procedure used to test hypothesis concerning the variance among 2 or more group means.
Because turkeys HSD is a conservative pairwise comparison, what is its effect on the critical values?
A turkey hsd produces larger values than snk and led tests
What do we do at stage 4?
At stage 4 we complete the f table and find the value of the test statistic
What is the 2nd calculation of stage 2- intermediate calculations?
The 2nd calculation of stage 2 ( intermediate calculations) is to divide the sum of the squared scores by the sample size Ex. (34.30)^2/10 + (33.00)^2/10 + (29.80)^2/10
What is the first calculation (1) we must make in stage 2 of intermediate calculations? How do we find it?
The first calculation (1) we must make in stage 2 of intermediate calculations is correction factor. we compute correction factor by squaring grand total (summation xt) and diving it by sample size (N)
What are the general steps to conducting a one way ANOVA?
The first step is to state the hypothesis, followed by setting the criteria, then you should compute the test statistic, and lastly you should make a decision. The third step (computing the test statistic) consits of four stages.
What is the formula for a test statistic for a one way ANOVA?
The formula for the Test statistic is Fobt= MsBG/MSE ( variance b/w groups)/ Variance within groups
What are the four assumptions made for a one way b/w subjects ANOVA?
The four assumptions made for a one way b/w subjects ANOVA are normality, random sampling, independence, homogeneity of variance
What are the four stages to commuting a test statistic?
The four stages to computing a test statistic: 1. preliminary calculations 2. Intermediate calculations 3. Compute the SS for each source of variation 4. complete the F table
What is unknown in an Anova test?
The population variance in one or more groups.
What does the proportion of variance estimate?
The porportion of variance estimates how much variability in the dependent variable can be accounted for by the level of factor.
When is the post hoc necessary?
The post hoc is required when the k>2 because multiple comparisons are needed
What are the two measure of proportion of variance?
The two measures of proportion of variance eta squared (r^2) and omega ( w^2)
What are the two sources of variation present in a one way b/w subjects ANOVA?
Variation attributed to difference b/w groups ( b/w subject variation) and variation attributed to error ( within subjects variation)
What is homeogentiy of variance?
We asume that the variance in each population is equal to that in the other
What is calculated in stage 3?
We compute the sum of squares (SS)
How do we calculate the variance or mean square error (MSE)?
We divide the SSE by the dfE.
For the third calculation of stage 2 intermediate steps, why don't we need to compute anything?
We do not need to compute for the third step because it simply involves restating the summation ^2 t
How do we find summation Xt?
We find summation Xt by first finding summation of x which is the sum of all scores - adding all scores together then taking the grand total as Xt
How do we summation x^2 for preliminary stage one?
We find summation x ^2 by squaring all the scores and then adding them
How do we find the sum of squares b/w groups (SSBG)?
We find the sum of squares b/w groups by using subtracting calculation 2 and calculation one in stage 2 - intermediate calculations.
How do we find the sum of squares total (SST)?
We find the sum of squares total (SST) by subtracting calculation 3 and calculation 1 in stage 2 intermediate calculations
How do we find the variance or mean squares between groups MSBG?
We find this value by dividing SSBG and DFBG
To help with the summations, Stage 1- preliminary calculations, recommends finding which two letters?
We must find k (levels of factors) and n (number of participants per group)
What do we need in order to calculate SSE(sum of squares error)?
We need SST And SSBG; We subtract sum of squares total (SST) and Sum of squares b/w groups
How do we find the standardized range statistic?
We need dfe and R(number of groups k)
How does one compute the test statistic for pairwise comparison?
We simply do the difference between the largest and smallest group mean
What is similar about finding degrees of freedom in a one way b/w subjects ANOVA?
We use K in both formulas of degrees of freedom
What is the purpose of computing the sum of squares (SS) in stage 3?
When we compute the Sum of squares (SS) we are obtaining the numerator for the variance formula.
How do you obtain/ find the critical values for a one way ANOVA?
You find critical values by using the F table and locating degrees of freedom numerator and degrees of freedom denominator
How do you find the last summation of preliminary stage one computations ( summation X2t)
You find summation x ^2t by adding all of the values obtained for summation x
How do you find the degrees of freedom for a one way b/w subjects ANOVA?
You find the degrees of freedom b/w groups and the degrees of freedom with group dfBG= K-1, dfE= N-K
What should you avoid doing when finding summation x^2 in the preliminary stage one?
You should never square summation x to find summation x^2
What is the difference between a test - wise and experiment wise alpha?
a test wise alpha is the probability of committing a type 1 error whereas experiment wise is the aggregated alpha or probability of committing type 1 error in multiple tests
How is the null hypothesis written and what does it mean?
o2u=0 the population means do not vary