1.4 One way ANOVA Flashcards
what is analysis of variance (ANOVA)
a statistical technique that is used to test for the significance of hypothesized group means difference
What type of data is ANOVA useful for? How many group means can you compare with ANOVA
experimental data
2 or more
In ANOVA the IV is referred to as?
factor
The conditions or groups of a factor are referred to as?
level of a factor
some important terms for ANOVA
Within-subject and between-subject variables
within-groups variations and between-groups variation
Analysis of variance (ANOVA) includes several different types of analyses, including
-One-way ANOVA,
-Factorial ANOVA,
-Repeated measures ANOVA for within-subjects data includes one or more factors
-Mixed ANOVA
-Analysis of covariance (ANCOVA)
-Multivariate analysis on variance (MANCOVA)
one-way ANOVA
used to compare two or more means of a single factor
involved assessing the effects of a single factor (IV) on the scores of a single dependent variable \
factor is categorical
DV is continuous
Factorial ANOVA
for between-subject data includes two or more factors (IVs)
Mixed ANOVA
includes both between-subject and within-subject factors
Analysis of covariance (ANCOVA)
is an extension of ANOVA that includes covariates as control variables
Multivariate analysis on variance (MANCOVA)
is an extension of ANOVA that allows for more than one dependent variable
in an ANOVA, If the factor has three or more levels, then the initial analysis is referred to as?
omnibus F test
in ANOVA what does a significant F ratio indicate?
that there are likely differences among the level means, but it does indicate which means are different
Follow-up analysis are needed to specify level differences
what is the F ratio? And what is its basic question
a signal to noise ratio…
The basic question is, is the variation between groups larger than the variation within groups?
If it is, then that difference is due to the treatment effect
Questions answered with one-way ANOVA
(list three at least)
Are there differences among the group means?
F ratio and p value
How large are the differences?
Eta squared effect size
How powerful was the F test?
What are the group means, standard deviations, and or standard errors?
What are the 95% confidence intervals that surround the group means?
Graphical representation of means
In ANOVA The null hypothesis (H0) is expressed as:
H0: µ1=µ2=µ3=…=µk
States that there are no difference level means
Alternative hypothesis (HA):
HA” “one or more levels is/are different”
No equation is needed
F ratio, which if it is large enough indicates. what is F ratio formula?
significant differences among group means
F=MSb/MSw
F= Inherent variance+treatment effect/inherent variance
Mean square error (within groups) and treatment (between groups)
MSb=SSb/dfb ; MSw=SSw/dfw
Degrees of freedom error (within groups), treatment (between groups), and total
dfb=K-1
dfw=k(n-1)
what is normality an assumption of?
that the distribution of the dependent variable are normally distributed for all levels of a factor
what indicates a violation of normality assumption?
Excessive skew or kurtosis indicate violations of the assumption
If distributions of all groups are non-normal in the same way, then violation is unlikely to have much of an effect
Homogeneity of variance
The variance among the three groups are not different from one another
o1=o2=o3=oe
Where e is the common variance between three conditions
ANOVA is usually robust to fairly large violations of the assumption
SPSS provides a test of this assumption
Partition of Sum of Squares(Variability)
SStot can be divided by in two part SSw and SSbet
