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PYB210 > 6. Multiple groups design and ANOVA > Flashcards

6. Multiple groups design and ANOVA Flashcards

1
Q

what are the reasons we have more than two groups in an experiment?

A
  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
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2
Q

why would we have more than two groups of interest in an experiment?

A

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

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3
Q

why is a control group important in an experiment?

A

to ensure internal validity

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4
Q

What does a control group do in an experiment?

A

serves as a benchmark to tell us if there IV is effective or not on the DV

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5
Q

what does it mean to de-confound a study?

A

Implementing another group to make a possible confounding variable an independent variable thus another condition in the experiment.

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6
Q

what can forming multiple groups in an experiment assist in?

A

refining out understanding of how an IV operates on our DV and allows us to evaluate the dose-response relatinship

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7
Q

what do multiple group experiments allow?

A

allows us to more clearly see the relationship between the IV and the DV

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8
Q

what are the common relationships between the IV and the DV?

A

linear, curvilinear and quadratic

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9
Q

how are the levels of the IV determine??

A

determined by type of relationship expected?

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10
Q

how many points of the IV are expected in a linear relationship?

A

at least three points

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11
Q

how many points of the IV are expected in a curvilinear relationship?

A

more than three

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12
Q

how far apart should levels of the IV be?

A

proportionately across the spectrum

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13
Q

what does having the levels of the IV proportionately spread across the spectrum allow?

A

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

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14
Q

when are t-tests needed?

A

when comparing two conditions only.

can be between subjects of within subject

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15
Q

what sort of samples are involved in between subjects t tests?

A

independent samples

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16
Q

what sort of samples are involved in within subjects t-tests?

A

paired samples or repeated measures

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17
Q

why cant we use t-tests for analysing multiple groups

A

you could… but the type 1 error rate would increase dramatically.
in each t-test, we are potentially wrong 5% of the time (p

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18
Q

what does an ANOVA do?

A

Tells us whether a difference exists somwhere between the group means.

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19
Q

what is an ANOVA referred to as?

A

the omnibus test

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20
Q

what was the basic objective of the independent groups t-test?

A

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

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21
Q

what is the statistic that is used to compare multiple group means?

A

t-ratio

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22
Q

what does the f ratio involve?

A

variance between groups (BG)

variance within groups (WG)

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23
Q

what is the variance between groups (BG) represening?

A

IV effect

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24
Q

what is the variance within groups representing?

A

sampling error

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25
Q

what is the f equation?

A

F = BG variance / WG variance

26
Q

the larger the f ratio…

A

the more likely it is to be significant

27
Q

when will F be larger?

A
  • 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
28
Q

why is WG considered error?

A

because participants in any group are considered to have been treated identically (remember random assignment to conditions, means pre manipulation groups considered equal)

29
Q

what will the the only two sources of variability in the data of a well designed experiment with a single IV?

A

variability due to the effect of manipulating the IV

variability dues to sampling error

30
Q

what is sampling error made up of?

A

differences in ability and circumstances + measurement errors

31
Q

what does ANOVA do to sources of variability and what can it tell us from this?

A

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

32
Q

how does ANOVA tell us that error is accountable for any apparent differences in scores BG?

A

looks at the ratio of variability between groups compared with the variability within groups

33
Q

how do we calculate between groups variability?

A

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

34
Q

how do we calculate the within groups variability

A

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

35
Q

what does the null hypothesis indicate?

A

that all group means are equal. IV has no effect on the DV

36
Q

what does the alternate (research) hypothesis indicate?

A

at least two group means are different. IV has effect on DV

37
Q

if the null hypothesis is true, what does this tell us about BG and WG variability?

A

BG variability is due to sampling error (E)
WG variability is due to sampling error (E)
THEREFORE:

BG = error (E)
WG = error (E)

BG/WG = error/error = 1

38
Q

if the research hypothesis is true, what does this tell us about BG and WG variability?

A

BG variability is caused by error and the effect of the treatment
WG variability is caused by error
THEREFORE:

BG = error + TREATMENT effect
WG = error

BG/WG = (E + treatment) / E = >1

39
Q

what does ANOVA tell us about the mean?

A

we analyse variability within groups and between groups to know whether group means are different

40
Q

how do you calculate variability?

A

SUM OF SQUARES divided by NUMBER OF OBSERVATIONS

∑ [(X-M)^2] / N

41
Q

what is the sum of squares apart of?

A

calculating BG or WG variability

42
Q

how do you calculate BG variability?

A

find the sum of squares of each group compared to the grand mean and then adding all of them together

43
Q

how do you calculate WG variability?

A

calculate SS for each group then add all the SS together

44
Q

what is the equation of computing the BG variability?

A

∑(M-GM)^2 x (number of data points in each group)

45
Q

what is the abbreviation of between groups SS?

A

SS_between

46
Q

what is the abbreviation for within groups SS?

A

SS_within

47
Q

what is SS_total?

A

the total variability in the data

48
Q

what is the equation for the total variability in the data?

A

SS_total = SS_between + SS_within

49
Q

what equation can express any one score on the dataset?

A

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

50
Q

what does GM stand for?

A

grand mean

51
Q

what is (M-GM)?

A

group mean - grand mean

the effect due to the group they were in

52
Q

what is (X-M)?

A

individual score - group mean

unexplained error

53
Q

why do we need to standardise SS_between and SS_within?

A

because they are based on different numbers of numbers so we do this to make them comparable

54
Q

how do we standardise the SS_between and SS_Within?

A

by dividing each SS by a degrees of freedom

55
Q

what is the result of standardising SS?

A

you get a Mean squares (MS)

e.g. SS_Between / df_Between = MS_Between

56
Q

what is the basic rule for df?

A

number of observations - number of parameters estimated

57
Q

what is the equation for df_total?

A

N-1

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

58
Q

what is the equation for df_between?

A

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)

59
Q

what is the equation for df_within?

A

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

60
Q

what is df_total?

A

df_between + df_within = dftotal

61
Q

what is the equation for MS?

A

SS/df

62
Q

what is the equation for F?

A

MS_between / MS_Within

PYB210 (11 decks)

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