Chapter 12- ANOVA Flashcards

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1
Q

When would you use an ANOVA vs. a t-test?

A

When you are examining more than two groups at the same time

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2
Q

What are the strengths of using an ANOVA over multiple t-tests?

A
  • Protects researches from excessive risk of a Type I error in situations when comparing more than two population means… automatically adjusts for the effect testing multiple hypotheses has on Type I errors
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3
Q

What is the logic behind the f-ratio?

A
  • Msbetween / Mswithin
  • Ms= mean squares (or MS values)
  • MSbetween measures the size of mean differences between samples
  • MSwithin measures the magnitude of differences expected without any effects of the IV
  • =obtained mean differences (including treatment effects) / differences expected by chance (without treatment effects)
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4
Q

Msbetween (between group variance)

A
  • measures the size of the differences between each level’s sample mean
  • the differences/variance between means can be cause by effects of the independent variable, or by random chance/sampling error

MSbetween= SSbetween / df between (K-1)

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5
Q

MS within

A
  • measures the size of the differneces that exist inside each of the treatment levels
  • Because the individuals in each group experienced exactly the same level of the independent variable, any variance within a sample cannot be cause by the independent variable’s effects
  • only explanation is random chance or sampling error
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6
Q

Hypotheses for ANOVA

A
  • Ho: μ1=μ2=μ3
  • H1: There is at least one mean difference
  • When H0 is true and there are no differences between levels, the F-ratio is balanced (when the effect of the IV i zero, the top and bottom of the F-ratio only measure random variance…. so we should expect an F-ratio near 1.00
  • When the F-ratio is near 1.00, we conclude that there is no significant effect of the IV…a large effect produces a large F-ratio
  • We reject the null hypothesis and conclude there is at least on significant difference between groups when we get a large F-ratio (far from 1)

All hypotheses in ANOVA are non-directional because F is a ratio of variances and variances cannot be negative (there is always a single tail to the distribution)

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7
Q

How to identify critical region?

A
  • Find where dfbetween (columns) and dfwithin (rows) intersect
  • Bold is for a=.01, normal is for 1=.05
  • dfbetween=k-1
  • dfwithin=n-k
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8
Q

Why are post hoc tests conducted after ANOVAs and do they tell you?

A
  • Hoc tests need to be conducted because ANOVA simply states that difference exists, it does not indicate which levels are different
  • Hoc tests determine exactly which groups are different and which are not
  • Tukey and Scheffe tests are common post hoc tests
  • Are done after an ANOVA where H0 is rejected
  • The tests compare the treatments two at a time to test the mean differences while correcting for concerns about experiment-wise Type 1 error inflation
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9
Q

How to calculate effect size for ANOVA?

A
  • compute the percentage of variance counted for by the independent variable
  • identified as η2
  • η2= SS between / SS total

.02-.12 is small effect, .13-.25 is medium effect, .26+ is large effect

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