Chapter 15: One Way ANOVA Flashcards
Analysis of Variance (ANOVA) uses ___ as the statistic to evaluate the null hypothesis.
- variance
The ANOVA is a test used to analyze experiments that have more than ___ groups.
- 2
We use the ___ test to tell us whether there is a significant difference between any of the groups.
- F test
What does the alternative hypothesis state?( think means as a hint)
at least one of the conditions has a different effect than at least one of the other conditions. Thus, at least one of the group means is different from at least one of the other group means.
What does the null hypothesis state?
the different conditions are all equally effective, so, scores in each group are random samples from populations having the same mean value. aka there is no difference between any of the groups means
U1=U2=U3
Is there always variability within data?
yes
The ANOVA splits the total variance into two sources. What are they?
SStotal =?
- within- groups variance (SSw)
- between groups variance ( SSbtwn)
- SStotal = SSw + SSbtwn
What is MSw and MSbtwn?
- MSw is the estimate based on the within-groups variance and MSbtwn is the estimate based on between-groups variance.
What is the decision rule?
- If Fobt> Fcrit, reject Ho
- If Fobt< Fcrit, retain Ho
List the steps in order to calculating a 1 way ANOVA! (6)
1. Calculate the sum of squares L> SSw, SSbtwn and SStotal 2. Calculate the degrees of freedom (df) L> dfbetween = K-1 (k=number of groups) L> df within = N-K L> df total= N-1 **also df total= df within + df between 3. Calculate Variance (MS) - MS btwn= SSbtw/dfbtwn - MS within= SSwithin/ df within 4. Calculate F obtained - Fobt= MSbtwn/MSwithin 5. Evaluate Fobt with Fcrit L> fcrit is found via.... Df btwn= numerator, df within= denominator ..... and alpha on table F. 6. Construct an ANOVA Summary Table
Layout of an Anova Summary Table?
Source SS Df MS Fobt Fcrit
Btwn —- — — — —
Within —- — — — —
Total —- —
On the ANOVA summary table how is significance shown?
- by the Fobt that is sig
If we decide we should reject Ho we have determined that the IV is having an effect on the DV. What is the next step?
- determine the size of the effect that the IV is having on the DV.
L> Omega Squared is a method to do this
What is the formula for omega squared?
SStotal + MSwithin
What is the criteria from Cohen to interpret effect size?
0.01-0.05 =small effect
0.06-0.13= medium effect
>0.14 = large effect
If you had an omega squared value of 0.742 what does this mean? (2)
- it means that the UV accounts for 74.2% of the variability in the DV. It also means that something else (unknown) accounts for 25.8% of the variability in the DV.
What is another method for determining effect size?
Eta Squared
Eta squared is similar or not similar to omega squared.
similar
Whats the difference between eta and omega squared?
- eta squared gives a more biased estimate of effect size. It usually gives an estimate of effect size larger than the true effect size.
What is the formula for eta squared?
SS total
What are the two assumptions underlying ANOVA?
- populations from which samples are taken are normally distributed.
- samples are drawn from populations of equal variance homogeneity of variance.
Anova is robust and generally insensitive to what?
violations as long as the sample size of the group (n) is equal.
Power varies directly with what?
L> relate it to Fobt too
- N
- as N increases, power increases.
- the larger the sample size (N), the larger Fobt will be
Power varies inversely with ?
L> relate to Fobt too
- sample variability
- as sample variability increase, the ability to detect a real effect decreases.
L> variability (MSwithin) is the denominator of the Fobt formula…if it is large…Fobt will be small.
Power varies directly with what?
hint …effect
- size of the real effect of the IV
L> ability to detect real effect (power) is greater for large effects
Explain a priori (planned) comparison!
- are specific comparisons that are planned in advance of the experiment . The comparisons are made according to the experimenters predictions. They are normally based on information obtained from previous research.
Explain Posteriori (post hoc) comparisons!
- not planned before the experimenter looks at the data collected from the experiment before deciding which groups to compare.
How do you calculate Planned comparisons?
- Independent T test to calculate it…. except we us MS since it is a better estimate of variance.
With planned comparisons we use Tobt so to determine if it significant we must use what?
- Tcrit which since we use MS within in the Tobt formula…we must use Df within (N-K) to find t crit…
What is the formula for independent T?
\/ 2MSwithin /n
Post hoc tests make ___ possible group comparisons and the comparisons are not what?
- all
- not based on previous research or a theory
What are the three types of post hoc tests?
- Tukey Honestly Significant Difference Test ( Tuky HSD)
- Newman Keuls Test (N-K)
- Scheffé
The Tukey HSD is designed to compare?
- all possible pairs of means
ex: an experiment with three groups
G1 mean to G3 mean
G1 mean with G2 mean
G2 mean with G3 mean
The Tukey HSD is based on what kind of distribution?
- Q distribution
- aka studentized range distribution
The Tukey HSD was developed by randomly taking ___ samples of ___n from the __ population. Comparisons are made by?
- K
- equal
- same
- subtracting the lowest mean value from the highest mean value
What is the formula for Tukey HSD?
Qobt= Xi - Xj
---------
\/ MS within /n
Xi = larger of the two means
Xj= smaller of the two means
MSw= within group variance estimate
n= number go subjects in each groupOnce you calculate Qobt for the Tukey HSD you must compare it to?
- Qcrit…..found on table G
L> found via….Df= within df
L> k = number of groups
L>alpha
The Newman keels (N-K) test is similar to the Tukey HSD but it differs via:
- It maintains the _____ rate at alpha; whereas, HSD maintains the _____ rate at alpha.
- comparison wise error
- experiment wise error
The Sheffé test is the most ____ of the post hoc tests.
conservative
Sheffé test is the most conservative post hoc because:
- it controls for Type 1 error by doing what?
- by doing all possible post hoc comparisons not just pair wise mean comparisons
ex:
Compare G1 with G2 and G3 combined or
Compare G2 with G1 and 3 combined etc
Sheffé test is the most conservative post hoc because:
- it limits the possibility of making a type 1 error to the alpha level for?
- all possible post hoc comparisons
Sheffé test is the most conservative post hoc because:
- although it can make combination comparisons how is it often also used?
- often used to make pair wise comparisons for extra type 1 error protection. This is done by using df between, Ms within and Fcrit from the ENTIRE ANOVA rather than just the groups being compared.
How do Tukey’s HSD and N-k control for type 1 error?
by making a complete set of pair wise comparisons however it cannot compare with the combination of other groups
Steps to calculating for Sheffé??
- Calc SSbetween groups ( groups i and j) for each comparison.
( SSbtwn= [SSi+SSj] - SSof both together ) - Calculate the MS between (i and j) for each comparison.
( MSbtwn= SSbtwn(i and j)/ dfbetween for entire ANOVA - Calculate Fscheffé for each comparison
Fscheffé = MS btwn (i and j)/ MS within (entire anova) - Evaluate F scheffé with F crit
Summary table set up for Scheffé test?
Groups SSbtwn df btwn anova MS btwn MS anova Fscheffé
