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Random Factors Flashcards

1
Q

how do you decide whether to use random factor analysis?

A

the decision depends on two things

  • how the study was designed
  • how you will interpret the findings
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2
Q

why are you more likely to get a statistically significant reslut if you treat analysis as fixed as opposed to random?

A

fk knows

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3
Q

whats the difference between fixed an random factors?

A

fixed

  • the levels of the experimental factor have been chosen purposely and carefully - very specific reason you made that choice
  • conclusions generated are apply only to these specific factors
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4
Q

whats the difference between fixed an random factors?

A

fixed

  • the levels of the experimental factor have been chosen purposely and carefully - very specific reason you made that choice
  • conclusions generated are apply only to these specific factors

random

  • the levels of the systematic factor have been chosen unsystematically i.e., random sampling from a wider population
  • in principle you could haev made others
  • conclusions generated apply to the wider population, beyond levels used
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5
Q

Both the experimental manipulation and the subject choice could be either fixed or random. Explain how?

A
  • experimental manipulation - the conclusions could be generated beyond the specific thing tested. E.g., that study on kids resisting marshmallows. are the findings generated applicable only to the act of resisting a marshmallow (fixed effect) or beyond this looking ta inhibitory control (random effect)
  • subjects - are you applying the conclusions generated ONLY to this sample (fixed effect) or the wider population (random effect)

so far in stats we have considered different analyses and these commonly assume the experimental manipulation is fixed and only the subject is random

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6
Q

if the experimental manipulatin in the ANOVA is treat as random - how would this affect the ANOA calculations?

A
  • by randomly sampling random b – we have introduced variability into the population estimates for factor a*
  • affected the means of factor A generated*
  • In stats we have to accommodate for this added variability. Whenever you have random factor design you have to add some sort of calculation to ensure your analysis is not bias (use the interaction terms as error)*
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7
Q

what does the f ratio tell us?

A

well the point of ANOVA is to compare variability due to experimental manipulations to the variability due to error

this is the basis of the f ratio =

effect + error/ error

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8
Q

in fixed effects anova (with only one subject treat as random) what does the f ratio compute

A
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9
Q

what would the f ratio come out as if you had no experimental effect?

A
  • If you have no experimental effect – expect this ratio to come out as one – because your comparing two error variances which should then be the same.
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10
Q

if there is an experimental effect how would this affect the f ratio?

A

if there is an experimental effect the f ratio would be greater than one

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11
Q

in fixed effects anova

A
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12
Q

how does the f ratio change with random effect ANOVA?

A

the overall logic of the ratio is the same, we have something due to an experimental effect something due to error

the difference is the denominator of the f ratio (how we calculate error)

  • The error term/variance* of any treatment effect includes the variability of every effect that influenced the treatment MS /treatment variance
  • so basically includes this random sampling process*
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13
Q

how would the error terms change for a one way ANOVA - for e.g., factor A?

for fixed vs random effects ANOVA?

A

how we calculate error (bottom part)

fixed

MS A (MS associated with factor A) / MS S/A (within group variability)

  • basically the between group vairance divided by within group variance
  • in SPSS labelled as MS within groups or MS error

random

  • exactly the same
  • that’s the beauty of a one factorial design
  • even though conceptually we know its different -
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14
Q

Error terms for fixed effects, two way anova?

factor’s A + B?

A
  • factor a and factor b + interaction effect
  • top part = mean square associated with the effect (a, b or interaction)
  • error term = the within group variance MS(s/ab)
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15
Q

Error terms for random effects, two way anova?

factor’s A + B?

A
  • factor a, factor + interaction effect
  • top part - MS a, MS b, interaction term
  • bottom part (error) - error term to test effect of a and b variance IS the interaction
  • error term for interaction - is the within groups variance
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16
Q

Error terms A (fixed) and b (random), two way anova?

A
  • a (fixed) - use the AB interaction
  • b (random) - use the within group variance
  • interaction term - use within group variance
17
Q

when error = mean squared of interaction term. what are some problems of this

A
  • interaction terms tend not to be good for error terms
  • not as good as the within-group variance
  • this is because they have fewer degrees in freedom which results in lower power
  • the fewer degrees of freedom, the harder it is to get into the desired p value (.5)
18
Q

when MS of the interaction term is used as the interaction term, this lowers power. how can we improve power?

A
  1. pooling
  • pool interaction terms, error terms etc
  • pooling increases your DF because you are adding up the DF. buying statistical power in this way
  • (modelling)
  • can only do such modelling when interaction terms are not significant - as soon as it becomes significant you shouldn’t pool it with anything else because there is an effect happening
  1. clever design and analysis
  • can design the experiment so that you gave many factors of the random variable
  • could trade that in for a lower number of data points (subjects per group) to keep sample sizes variable
  • the more conditions you have a of a particular variable the more DF we have - this increases power
19
Q

things to consider when creating a fixed and random effects design

A
  • maximise the number of n per condition
  • balanced design - assign things equally

ranodm

  • maximise the levels of your random variable
20
Q

why do we need more levels in the random effects factor

A

Its for power.

  • So the interaction term, the mean square (AxB) will be your error term.
  • Thus the quantity that you use to test the effect of a.
  • The more levels you have in your factor B – the more degrees of freedom you have in your interaction term (translates to more statistical power).
21
Q

fixed and random effects apply the same way as we learned in meta analysis

A
22
Q

why are results less likely signifiant with random effects

A

because the degrees of freedom for hte error term ARE now the DF of the error term. Ends up being a small number

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