Bivariate Analysis: Independent T-Test and ANOVA Flashcards
What is an Independent T-Test?
Measures a Continuous variable and compared across two Discrete independent groups
What is a Two Group Comparison research design entail?
1 Group receives an experimental treatment
1 Group receives a placebo or usual care
What does the independent variable measure in an Independent T-Test?
Discrete, nominal
What does the dependent variable measure in an Independent T-Test?
Continuous, ratio
What factors influence the size of t in an Independent T-Test?
- Difference between the means (X1-X2)
- Variability (sp2)
- Sample Size (n)
How does the Difference between the Means change t?
As the difference between the mean increases, the value of t increases
How does the Variability change t?
As variability value increases, the value of t decreases
How does the Sample Size change t?
As the sample increases, the value of t increases
In an Independent T-Test the hypothesis includes what?
The comparison of means between independent groups
What is an ANOVA test?
Measures a continuous variable, compared across 3 or more Discrete Independent groups
ANOVA is a 2 Step Process, what are the steps?
- Test for differences among the group means
- If yes, then a follow up test to identify which specific groups are different from one another
What are the assumptions that must be made to complete an ANOVA test?
- Random Samples
- Independent Samples
- Independent observations within groups
- Normally distributed data
- Equal variances
What is the first step of the ANOVA?
F Test for H0: no difference among group means
The F Test for H0 looks at what?
F-Statistic
P-Value
If p-value is less than significance level, reject H0
What is the second step of the ANOVA?
Post Hoc* Test
The Post Hoc* Test is what?
Modified version of T-Test, pairwise comparisons
Post Hoc = After the event
What is a Familywise Type 1 Error Rate?
The probability of making at least one type 1 error when multiple tests are conducted on the same variable in independent samples increases with each additional test
What tests corrects for the Familywise Type 1 Error Rate?
Post Hoc
What does the HA of an ANOVA test suggest?
At least ONE population mean does not equal another population mean
If you reject the null hypothesis, you can conclude that at least one population mean is different but it cannot conclude that ALL of the population means are different? You must use what test to analyze this?
Post Hoc, used to determine which specific means are different
What are the 2 sources of Variance in an ANOVA test?
- Between: variance between the various groups
- Within: variance within each group
What is the Total Variance?
Variance between groups + Variance within groups
How do you partition variances?
Alleviate negative numbers by squaring
Sum of squares
What is SSB?
Sum of the square differences BETWEEN the group means and the grand mean
How do you calculate the SSB?
- Subtract grand mean from each group mean and square
- Sum the numbers
- Multiply the sum by the sample size
SSB contains what information?
EFFECT
aka treatment effect
What is SSW?
Sum of all the square differences between individual data and the group mean WITHIN each group
How do you calculate the SSW?
- Calculate each group mean
- Subtract individual observation from its group mean and square
- Sum all numbers
SSW contains what information?
ERROR
takes into account the error within the groups
What is the partitioning of the sum of squares?
SSB (SSEffects) + SSW (SSError) = SS (Total)
What is MSB?
Mean Square Between Groups
What does MSB describe?
Average deviation of group means from the grand mean
How is MSB calculated?
Unbiased estimate of error variance plus treatment
What is MSW?
Mean Square Within Groups
What does MSW describe?
Average deviation of means from their group mean
MSW = MSE, which is what?
Mean Square Error
How is the F-Statistic calculated?
F Stat = MSB/MSW
For any treatment to have an effect, F must be greater than what?
Greater than 1, cannot be negative
F Statistic represents what?
Ratio of treatment effect to error
If the population means are equal, the sample means will be close together suggesting what type of data?
- Sample means will be close to grand mean
- SSB and MSB will be small if population means are equal
- Small F Stat
If at least one population mean is quite different, the corresponding sample mean will be different suggesting what type of data?
- Corresponding sample mean will be different from grand mean
- SSB and MSB will be large
- Large F providing evidence against H0
How large is F Stat required to be in order to reject H0?
- Determine by F Critical Value associated with DF and Alpha
- Determined by the p-value associated with the calculated f-stat (Large F = small p-value)
ANOVA F-Tests are ALWAYS ONE SIDED for determining what?
P-Value
But for an ANOVA can a one sided HA be used?
NO, must be 2 sided
What is Eta-Squared n^2?
Tells you the strength of the relationship between independent and dependent variables
Eta-Squared percentage reveals the variance that can be explained
ex. Eta=22%
100-22 = 78
78% of variance results from other factors
