brudaa Flashcards
What is ANOVA
Analysis of variance
What does ANOVA test
Mean difference for one or two independent variables with at least 2 levels/groups
ex. Are there differences in level of engagement in student organizations across the different schools in ADMU
Why not just use multiple t-tests?
T-test can only test difference between 2 groups at once
it would take a lot of steps to reach final conclusion
The more tests we do, the higher the possibly of splitting an error in making decisions
1 ANOVA test will lead to only 1 error statistic
an increase of decision points adds up risk and compounds alpha values
What are the types of ANOVA tests
One way ANOVA - one independent variable with at least 2 groups/levels. one dependent variable (continuous)
Two way ANOVA - two independent variables with at least 2 groups/levels. one dependent variable (continuous)
Repeated measures ANOVA - one independent variable with three related levels; sample mean measured across three time points/conditions. One dependent variable (continuous)
What are examples research questions of One-way, Two-way, and repeated measures ANOVA
One-way: Is there a significant difference in the number of coffee cups consumed daily across different year levels of undergrad students in ADMU
Two-way: Is there a difference in frequency of using physical punishment for fathers and mothers belonging to different socioeconomic classes
Repeated Measures: Is there a difference in the level of stress of parents joining a program from baseline, to 3 months follow up, and 6 months follow up
What is a one way anova
a non directional procedure that tests the equality among 2 or more means using independent groups; scores are compared to the mean
Two variables - one independent variable: nominal with 3 or more groups, one dependent variable: continuous (ratio/interval)
Main question: Does the grouping of IV have an effect on their scores/feelings/expression of the dependent variable
What does one way ANOVA look at
ANOVA looks at the variations in a set of scores across two components:
Variation within levels/groups (deviation of raw scores from their own groups)
Variation between groups (deviation of group means from one another); how spread out the different group means are from one another
Where does our decision depend on in one way ANOVA test
In hypothesis testing, decision depends on whether the score distribution of groups are separate enough to conclude that groups are significantly different from one another
not all groups have to differ from each other; even one group differing can conclude that there is a difference
What is logic of One way ANOVA
Comparing means using ANOVA entails analysis of the ratio of between groups variation and within groups variation
Variation between groups - distance or deviation of group means from one another
Variation within groups - distance or deviation of raw scores from their group means
What do no overlaps in the graph (score distributions are separate) state?
Suggest that the IV may have an effect (significant effect)
it shows that the scores are different from each other implicating that there is a difference between groups.
what do overlaps in the graph (score distributions are not separate) suggest?
It suggests that the IV may not have an effect
it shows that the scores do not differ from each other. It overlaps with one another since the scores did not significant differ from each other stating that there is no significant difference.
What is between groups variance
Spread of the mean between groups
effect of treatment or the independent variable
shows the differences BETWEEN groups
large value = bigger difference between groups
what is within groups variance
spread of the scores within each group
effect of individual differences, unexplained external factors, and error
larger value = larger spread of scores within a group
How to obtain a significant result
the effect of the IV (variation between groups) must be significantly larger relative to the within groups variance; graphs should be not overlapping
a larger obtained F ratio that exceeds the F critical will be an outcome from a between groups variance value being higher than a within groups variance
What are assumptions for One way ANOVA
The IV is categorical and has two or more levels
DV is continuous
Independence of observations: each observation of the DV is independent of the other observation of the DV. The score of one participant does not influence another
Normality - sampling distribution of differences between means is normal
Homogeneity of variance (homoscedasticity): variance should be the same across groups
What do we have to note on violations of assumptions
Violations of normality do not affect, or minimally affect, the validity of the ANOVA as long as the sample is at least 30
Violations of homogeneity do not affect or minimally affect the validity of the ANOVA when groups are large and equal in size
What are the first 2 steps in hypothesis testing
- State the Hypothesis -
Ho: There is no difference among the groups means - non directional hypothesis
Ha: There is a difference among the group means - at least one mean is different from the others
- Set the level of significance
Alpha level of 0.5
What is the third step in hypothesis testing
Solving for test statistic
(in order)
calculate grand mean
obtain degrees of freedom
obtain F score -
SS between, SS within, (checkpoint) SS total
MS between and MS within
Obtain F-ratio by dividing MS between by MS within
Why do we need to calculate the grand mean
Due to multiple pairs of comparison, there will be multiple mean differences to be tested
the grand mean provides a standard value from which we can test our sample mean against
Nk - the sample size for each sample mean
What is df between
use of a df that takes into consideration the grand mean
using individual sample means as the values that compromise the grand mean
df between: k-1 (k = number of groups)
what is df within
controls for sample size
takes into account that there are multiple groups
df within: Ntotal - k
(Ntotal = number of sample
k = number of groups)
How do we get F score
F-table
F distribution looks at proportions of variance explained by effect of differences and variance unexplained due to random error or sampling
F ratio = Effect/Error
(Effect = MS between
Error = MS within)
What is an optional step to check if SS within and SS between is correct
getting the SS total; shows us the total variance (representation of the overall randomness of all values)
equal to the sum of SA between between and SS within
to solve for SS within, just subtract SS between from SS total and vise versa to get SS between.
what is the last step in hypothesis testing
Making a decision
If computing: Compare the obtained F score to the critical F score from table D
to determine F critical you need to refer to:
df between = numerator
df within = denominator
Obtained F score > Fcrit = reject the null hypothesis (Ho): Conclude that mean levels of the groups are not equal
