Flashcards in 6. Multiple groups design and ANOVA Deck (62):
what are the reasons we have more than two groups in an experiment?
1. ore than two groups of interest
2. examining multiple treatments
3. de-confoundng a study
4a. refining our understanding
4b. Looking for nature of relationships
why would we have more than two groups of interest in an experiment?
When we need to identify the difference between more than two groups.
e.g. schizophrenia suffers show impaired cognitive performance when compared to controls. Does this mean tht impaired cognitive performances can lead to schizophrenia? or is schizophrenia the only disorder leading to cognitive impairment?
May wish to determine whether difference exists between schizophrenic and depressed individuals therefore study with: schizophrenics, depressed and controls
why is a control group important in an experiment?
to ensure internal validity
What does a control group do in an experiment?
serves as a benchmark to tell us if there IV is effective or not on the DV
what does it mean to de-confound a study?
Implementing another group to make a possible confounding variable an independent variable thus another condition in the experiment.
what can forming multiple groups in an experiment assist in?
refining out understanding of how an IV operates on our DV and allows us to evaluate the dose-response relatinship
what do multiple group experiments allow?
allows us to more clearly see the relationship between the IV and the DV
what are the common relationships between the IV and the DV?
linear, curvilinear and quadratic
how are the levels of the IV determine??
determined by type of relationship expected?
how many points of the IV are expected in a linear relationship?
at least three points
how many points of the IV are expected in a curvilinear relationship?
more than three
how far apart should levels of the IV be?
proportionately across the spectrum
what does having the levels of the IV proportionately spread across the spectrum allow?
allows for clear examination of the levels of the IV. This only applies to the levels of the IV that are based on measurements rather than categories
when are t-tests needed?
when comparing two conditions only.
can be between subjects of within subject
what sort of samples are involved in between subjects t tests?
what sort of samples are involved in within subjects t-tests?
paired samples or repeated measures
why cant we use t-tests for analysing multiple groups
you could... but the type 1 error rate would increase dramatically.
in each t-test, we are potentially wrong 5% of the time (p
what does an ANOVA do?
Tells us whether a difference exists somwhere between the group means.
what is an ANOVA referred to as?
the omnibus test
what was the basic objective of the independent groups t-test?
to determine whether the difference seen between two group means is large enough for us to be reasonably convinced that it is not due to random error or chance
what is the statistic that is used to compare multiple group means?
what does the f ratio involve?
variance between groups (BG)
variance within groups (WG)
what is the variance between groups (BG) represening?
what is the variance within groups representing?
what is the f equation?
F = BG variance / WG variance
the larger the f ratio...
the more likely it is to be significant
when will F be larger?
- when the difference between 'at least some' groups is large this increases our BG
- the difference within groups (or our sampling error) is small, this decreases our WG
why is WG considered error?
because participants in any group are considered to have been treated identically (remember random assignment to conditions, means pre manipulation groups considered equal)
what will the the only two sources of variability in the data of a well designed experiment with a single IV?
variability due to the effect of manipulating the IV
variability dues to sampling error
what is sampling error made up of?
differences in ability and circumstances + measurement errors
what does ANOVA do to sources of variability and what can it tell us from this?
it isolates and quantifies these sources of variability in our data to see if sampling error alone can account for any apparent differences in scores between groups
how does ANOVA tell us that error is accountable for any apparent differences in scores BG?
looks at the ratio of variability between groups compared with the variability within groups
how do we calculate between groups variability?
by looking at how many group means vary around the grand mean (AKA the overall experiment mean)
between groups variability is calculated from variations in the mean scores between levels of the IV
how do we calculate the within groups variability
calculate the variance for each group separately, that is calculating the variance of individual scores around their group mean.
In other words, within groups variability is calculated from variations between the scores of participants treated alike i.e. within each condition
what does the null hypothesis indicate?
that all group means are equal. IV has no effect on the DV
what does the alternate (research) hypothesis indicate?
at least two group means are different. IV has effect on DV
if the null hypothesis is true, what does this tell us about BG and WG variability?
BG variability is due to sampling error (E)
WG variability is due to sampling error (E)
BG = error (E)
WG = error (E)
BG/WG = error/error = 1
if the research hypothesis is true, what does this tell us about BG and WG variability?
BG variability is caused by error and the effect of the treatment
WG variability is caused by error
BG = error + TREATMENT effect
WG = error
BG/WG = (E + treatment) / E = >1
what does ANOVA tell us about the mean?
we analyse variability within groups and between groups to know whether group means are different
how do you calculate variability?
SUM OF SQUARES divided by NUMBER OF OBSERVATIONS
∑ [(X-M)^2] / N
what is the sum of squares apart of?
calculating BG or WG variability
how do you calculate BG variability?
find the sum of squares of each group compared to the grand mean and then adding all of them together
how do you calculate WG variability?
calculate SS for each group then add all the SS together
what is the equation of computing the BG variability?
∑(M-GM)^2 x (number of data points in each group)
what is the abbreviation of between groups SS?
what is the abbreviation for within groups SS?
what is SS_total?
the total variability in the data
what is the equation for the total variability in the data?
SS_total = SS_between + SS_within
what equation can express any one score on the dataset?
X = GM + (M-GM) + (X-M)
so we assume everyone starts at the grand mean, then we add the effect due to the group they were in then add any unexplained error
what does GM stand for?
what is (M-GM)?
group mean - grand mean
the effect due to the group they were in
what is (X-M)?
individual score - group mean
why do we need to standardise SS_between and SS_within?
because they are based on different numbers of numbers so we do this to make them comparable
how do we standardise the SS_between and SS_Within?
by dividing each SS by a degrees of freedom
what is the result of standardising SS?
you get a Mean squares (MS)
e.g. SS_Between / df_Between = MS_Between
what is the basic rule for df?
number of observations - number of parameters estimated
what is the equation for df_total?
based on the number of individual scores contributing to the gran mean
N = number of observation which is the total number of people
1 = the number of parameters estimated
what is the equation for df_between?
number of groups - 1
based on group mean - grand mean
number of observations are the number of groups
Number of parameters estimated is 1 (grand mean)
what is the equation for df_within?
N - number of groups
based on individual scores - group mean
Number of observation are total number of people (N)
parameters being estimated are per group thus number of groups
what is df_total?
df_between + df_within = dftotal
what is the equation for MS?