Session 4b Flashcards
Prior requirements/assumptions of one way ANOVA
The population distribution of the DV is NORMAL within each group The variance of the population distributions are equal for each group (HOMOGENEITY OF VARIANCE ASSUMPTION)
Independence of observations
The assumptions about normality and equal variances are assumptions about what
the population
The assumptions about normality and equal variances are assumptions about the population
Usually the best we can do is examine the what
sample for evidence about whether these assumptions hold
what re the methods for assessing normality
Descriptive and Inferential Statistics:
Tests for skewness
K-S and Shapiro-Wilk tests
Visual methods:
Histograms
Normal Quantile (Q-Q) Plot
what is Skewness
represents symmetry and whether the distribution has a long tail in one direction
Look at descriptive statistics
Skewness should be what
≈= 0
> 0 skewness indicates what
positive/right skew
< 0 skewness indicates what
negative/left skew
what does the The Shapiro-Wilk test do
Compares sample scores to a set of scores generated from a normal distribution with the sample mean and standard deviation
what is the Limitation of the normality tests
It is easy to find significant results (reject null hypothesis that data is normal) when sample size is large
what should you do inanition to the normality tests
plot the data
Separate histograms for each group to assess normality: what to look for
Look for obvious signs of nonnormality
Does not have to be perfect, just roughly symmetric
what is the problem with constructing plots
Can be difficult to assess visually
how to Evaluate a normal quantile plot (or normal probability plot) (the graphs)
Sort observations from smallest to largest
Calculate z-scores for the sorted observations
Plot the observations against the corresponding z-scores
If the data are close to normal, then the points will like close to a straight line
Serious violation of Assessing homogeneity of variance tends to inflate what
the observed value of the F statistic
aka Too many rejections of H0 (high Type I error)
why can we not just do the Fmax test for homogeneity of variance
Easy to compute, but assumes that each group has an equal number of observations
what does the Levene’s test test
homogeneity if variance; Tests the null hypothesis that the population variances are equal
what does the levee’s test measure
It measures how much each score deviates from its group mean
for levene’s test, It is very easy to obtain significant results when what
the sample size is large
If normality and homogeneity of variances is not met. . what should we do
A data transformation may be useful
A data transformation may be useful to. .
make data less skewed
make heterogeneous variances more homogeneous
If data transformation does not help meet assumptions, what should we do
consider nonparametric tests
what is the nonparametric tests
Kruskal-Wallis ANOVA
Assessing independence of observations (an assumption of one way anova) why bother doing this
Knowing the value of one observations gives no clue as to that of other observations
Independent observations:
Knowing the value of one observations gives no clue as to that of other observations
This is one of the most crucial assumptions underlying what test
the F test
It is difficult to predict how bad the F test will be if what is violated
independence of observation
is there an easy way to fix the F test when this assumption is violated
no
is there easy test for non-independence
no!
what can give some clues regarding this assumption (independence of observations)
Knowledge of how data was collected
Example: suppose instead of sampling individuals randomly from a population, we sample pairs: a participant and their best friend The responses of pairs may be similar to each other and NOT independent
Any solutions? (for independece of observations)
Experiments should be carefully designed to avoid non-indepndent observations
Random sampling and random assignment should be applied as much as possible
what are the steps for One way anova
Assure independence of observations
Check normality and equal variance assumptions
Create ANOVA summary table
If H0 is rejected, conduct multiple comparisons for pairs of means as necessary/desired
