test 4 one way randomized anova Flashcards
Researches may choose to use a design with an more than two levels for what three reasons?
- the can compare multiple treatments
- they can compare multiple treatments with no treatment
- the can compare placebo group with control and experimental groups.
Using 3 different experiments to compare 3 levels will increase what type of error?
Type 1 error rate
means we reject the null when we should have failed to reject it
What would the type one error be for an experiment with 3 levels and an alpha of .05?
1-(1-a)^c a=alpha, c=number of levels 1-(1-.05)^3 1-(1.05)^3 1-.95^3 1-.86 =.14 so, the probability of a type one error on atleast one of the three tests is 14%
One way of counteracting the increased chance of a type 1 error is to use a more stringent alpha level. The _________, in which the desired alpha level is divided by the number of test or comparisons, is typically used to accomplish this.
Bonferroni adjustment
What would the Bonferroni adjustment be for a test with 3 levels and an alpha of .05?
.017
A more stringent alpha decreases the _______ and increases the ________.
decreases the Type I error and increases the Type II error.
A better method for comparing 3 levels or more is to use _______ to compare all groups rather than doing 3 experiments.
a single statistical test - the ANOVA (analysis of variance)
A placebo group allows for a more accurate assessment of a therapy’s effectiveness because, in addition to spontaneous remission, it controls for _________.
participation expectation effects
Imagine that a researcher wants to compare four different types of treatment. the researcher decided to conduct 6 different studies to make these comparisons. What is the probability of a Type I error, with alpha = .05? Use the Bonferroni adjustment to determine the suggested alpha.
1-(1-a)^c a=alpha, c=number of levels 1-(1-.05)^6 1-.95^6 1-.735 .26.5 26.5%
The Bonferroni adjustment would be .008 for each level.
(.05/6) = .008
An inferential statistical test for comparing the means of three or more groups.
ANOVA
______ subjects design has different participants in each group.
______ subjects design has the same people in each group.
between = different ppl within = same ppl
When the design is a between-subjects design, we use a __________ statistical test.
one-way randomized ANOVA
An inferential statistical test for comparing the means of three or more groups using a between-subjects design and one independent variable.
one-way randomized ANOVA
The term “one-way” indicated that the design uses _____.
only one independent variable
The term “randomized” indicates that participants are ______.
randomly assigned to conditions in a between-subjects design.
The null hypothesis for an ANOVA is that the sample means represent _______.
the same population
Ho: µ1 = µ2 = µ3
The alternative hypothesis of an ANOVA is that the sample means represent ______.
different populations
Ha: at least one µ ≠ another µ
The mean performance across all participants in a study is the ________.
grand mean
The amount of variability among the scores cased by chance or uncontrolled variables.
error variance
We are interested in whether the variability of means is due primarily to the IV, or to _______.
error variance
The error variance can be estimated by looking at the amount of variability _____ each condition.
within
The variance within each condition; an estimate of the population error variance.
within-group variance
An estimate of the effect of the independent variable and error variance.
between-groups variance
The systematic variance between the groups could be due to the _______ or to the _______.
the effects of the Independent variable (variance due to the experimental manipulation) or due to the influence of uncontrolled confounding variables (variance due to extraneous variables).
The ration of between-groups variance to within-groups variance.
F-ratio
If the IV had no effect, any variance between group means would be due to _____.
error
The F-ratio will help to determine whether most of the variability is attributed to _________ (hopefully due to the IV and not to confounding variable) or to chance and random factors (error variance).
systematic variance
What is the formula for F?
F = btwn-groups variance
————————————— =
within-groups variance
error variance
For an F-ration to be significant (show a statistically meaningful effect of an independent variable), it must be substantially greater than _____.
1
If an F-ration is approximately 1, then the btw-groups variance equals the wthn-groups variance and there is ____________ of the IV.
no effect
The sum of squared deviations of each score from the grand mean.
total sum of squares (ssTotal)
_
∑ (X- XG) ^2
For SS total:
X represents ____
_
XG represents _____
∑ = ______
- each individual score
- the grand mean
- sum of all of the deviation scores you get in the ()
The sum of squared deviations of each score from its group mean and is the reflection of the amount of error variance within each condition.
within-groups sum of squares
_ ∑ (X- Xg) ^2
For SSwithin:
X represents: _____
_
Xg represents _____
∑ = _____
- each individual score
- the mean for each group or condition
- sum of all of the deviation scores you get in the ()
The sum of the squared deviations of each group’s mean from the grand mean, multiplied by the number of subjects in each group.
between-groups sum of squares
SSbetween =
Xg =
XG =
n =
∑ [(Xg-XG)^2 x n] = ssbetween
Xg = mean for each condition
XG = grand mean
n= number of participants in each group
The __________ is an indication of the systematic variance across the groups (the variance due to the IV and any confounds) and error.
between groups variance
If you add sswithin and ssbetween, it should equal ________.
sstotal
An estimate of either variance between groups or variance within groups.
mean square
To get the mean square, you divide each ___ by the appropriate ______.
SS
df
dfTotal =
N-1
N= total number of participants in study
the dfTotal for a study with 24 participants would be
N-1
24-1
23
dfWithin =
N-k
N = number of total participants
k = number of groups or conditions in the study
the dfWithin for a study with 3 groups of 8 people in each group is:
dfWithin = N-k
24-3
24-3 = 21
dfBetween=
k-1
k = number of groups
The dfBetween for a study with 24 people and 3 groups is:
k-1
3-1
2 = dfBetween
To check your calculations of df, the sum of ______ and _______ = _______
dfWithin and dfBetween = dfTotal
Find the MS between
SSbetween = 65.33
dfBetween = 2
Find the MS within
SSwithin = 62
dfwithin = 21
65.33/2 = 32.67 = MS between
62/21 = 2.95 = MS within
F = _____
find F is MS between = 32.67 and MS within = 2.95
MS between/MS within
32.67/2,95 = 11.07
To find the critical F value, we use :
df within (down left side) df between (running across top)
If F (F obtained) exceeds Fcritical, we _______.
reject the null
it is statistically significant at the .05 level
If F(2,21) = 11.07, p
the 2 = df between groupd
the 21 = df within groups
This means that we reject Ho and support Ha, at least one group differs significantly from the others.
It is useful to know how much of the variability in the DV can be attributed to the IV. In other words, it would be useful to have a measure of _______.
effect size
An inferential statistic for measuring effect size with an ANOVA.
eta-squared (n^2)
n is italicized
n^2=
effect size
SSbetween / SStotal
When used with ANOVE, a means of comparing all possible pairs of groups to determine which ones differ significantly from each other.
Post hoc tese
A post hoc test used with ANOVA for making all pairwise comparisons when conditions have equal n’s
HSD
if there are not equal participants in each group then you would use what post hoc test?
Fischer’s protected t test
An estimate of the variance of the group means about the grand mean; includes both systematic variance and error variance.
between-groups variance
An estimate of the variance within each condition in the experiment; also known as error variance, or variance due to chance.
within-groups variance
A measure of effect size- the variability in the dependent variable attributable to the IV.
eta-squared (n^2)
if the group means are 4, 3.88,, and 4, and the grand mean is 3.96
Do you think the within and between group variances are large, moderate, or small? will the corresponding f-ration be equal to or greater than or less than 1?
both within and between groups variances are moderate to small. this should lead to an f-ratio of approximately 1.
of the following 4 ratios, which appears to indicate that the IV had an effect of the DV? 1.25/1.11 .95/1.25 1.95/.26 .52/1.01
The F-ratio 1.95/.026 suggests that the IV had an effect on the DV.
(difference is greater than .5)
