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SRM > ANOVA > Flashcards

ANOVA Flashcards

1
Q

What is ANOVA

A

Also known as Analysis of variance.
* Is used when there are more than two sample population, on which statistics have to be performed.
When there are more than two groups of sample population, this method has a tactical advantage over t-test.
* In the context of ANOVA, the independent factor is termed as ‘factor’.
- greater flexibility in designing experiments

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2
Q

Multiple t test vs one way anova

A

ANOVA tests k groups (typically 3 or more) together in one model. Thus, no matter how many different means are being compared, ANOVA
uses one test with one alpha level to evaluate the mean differences, and
thereby avoids the problem of an inflated experiment-wise alpha level.

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3
Q

Increase of type 1 error

A

Each test has a risk of a Type I error, and the more tests you do, the more risk there is.
Meaning it makes it more likely to reject the null and detect an effect of the IV, where
there isn’t any.

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4
Q

experimentwise alpha

A

The probability of that an experiment will produce any TYPE I error is called experimentwise alpha (αEW)

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5
Q

When will the experimentwise alpha be larger than the alpha

A

When t-tests are performed freely in a multi-group experiment, the experimentwise alpha (αEW) will be larger than the alpha used for each t test.

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6
Q

When will the experimentwise alpha increase?

A

will increase as the number of groups increases because of the increasing number of opportunities to make a TYPE I error

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7
Q

Experimentwise alpha = ?

A

= 1-(1-α)^j

a = significance level chosen for an experiment.
*
j = number of groups.

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7
Q

Variables in a one way ANOVA

A
  • One categorical independent or quasi-independent variable (technical name: factor)
    with at least two independent groups (technical name: levels).
  • One DV - continuous variable (e.g., achievement test scores).
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8
Q

Null Hypothesis

A

There are no differences among the populations (or
treatments). The observed differences among the sample means are caused
by random, unsystematic factors (sampling error) that differentiate one
sample from another.

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9
Q

Alternative hypothesis

A

The populations (or treatments) really do have
different means, and these population mean differences are responsible for
causing systematic differences among the sample means.

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10
Q

Between treatment variance measures

A
  • Systematic treatment effects
  • Random unsystematic factors
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11
Q

Within treatment effects

A

Measures differences caused by random, unsystematic factors

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12
Q

The two basic components of the analysis process

A

Between-
Treatments Variance and Within-Treatment Variance.

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13
Q

When the F ratio is 1

A

there are no systematic treatment effects,

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14
Q

When the f ratio numerator is greater then the denominator

A

When the treatment does have an effect,

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15
Q

SSB

A

*This is the sum of the squared differences between each group mean and the grand mean.

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16
Q

SSW

A

*This is the sum of the squared differences between each individual observation and the
group mean of that observation.

17
Q

SST

A

*This is the sum of the squared differences between each individual observation and the
grand mean.

18
Q

df for between groups

A

The between group df is one less than the number of groups (k-1)

19
Q

df for within groups

A

The within group df is the sum of the individual df’s of each group (N-k)

20
Q

df for total

A

The total df is one less than the sample size (N-1)

21
Q

What is MS equal to

A

“mean of the squares” OR mean of
squared deviations OR variance

22
Q

Assumptions of a one way ANOVA for an independent samples design

A
  • Independent random sampling
  • Normal distributions.
  • Homogeneity of variance.
    (i.e., The populations from which the samples are selected must have equal variances)
23
Q

Methodology of using ANOVA

A

State the hypothesis
* Select the statistical test and the significance level (alpha level). - one-way ANOVA, alpha level =0.05
- Select the sample and collect the data
- Find the region of rejection
·Calculate the test statistic
*Make the statistical decision.

24
Q

Post hoc tests

A

additional hypothesis tests that are done
after an ANOVA to determine exactly which mean differences are significant and
which are not.

25
Q

Post hoc tests are done when

A
  1. You reject H0
    and
  2. There are three or more treatments (k > 3).
26
Q

Making multiple pairwise comparisons

A

a post hoc test enables you to go back through the data and compare
the individual treatments two at a time.

27
Q

Multiple comparisons

A

Some of the available methodology are:
Fischer’s protected t-test
* Bonferroni correction
* Scheffe’s test
* Fischer’s Least Significant Difference (LSD)
* Tukey’s Honestly Significant Difference (HSD)

28
Q

Bonferroni correction (Dunn’s test)

A

This type of test is applicable in performing multiple t-tests.
The idea is to re-define alpha value (significance level) while performing multiple comparisons.
Based on work done by Bonferroni, it can be stated that for a given number of comparisons (j), the experimentwise alpha (αEW) will never be more than j times alpha used for each comparison.

29
Q

Two way ANOVA

A

The two factor design moves that one step closer to reality by testing the effects of
two independent variables (‘factors’) on a dependent variable simultaneously.

30
Q

Mixed design ANOVA

A

Where both unrelated and related factors are involved

31
Q

Main effect

A

Where both unrelated and related factors are involved

32
Q

Interaction effect

A

the effect of one IV changes across the
different levels of the other IV.

33
Q

Assumptions of a two way ANOVA

A
  • Homogeneity of variance
  • DV on interval scale
  • Sampling distribution of means is normal; assumed by checking that dependent variable is normally distributed.
34
Q

Repeated measures ANOVA

A

research design that involves multiple measures
of the same variable taken on the same or matched subjects either under
different conditions or more than two time periods.

35
Q

Complete crossed factorial design

A

ANOVA applied to an experiment having more than two factors by combining them (factors) in definite combination
⚫ This type of design performs ANOVA in all possible combinations of factors.
⚫ It is also known as factorial design.

36
Q

Balanced design

A

When different combination of factors in ANOVA are represented by same number of samples

37
Q

Factorial designs are represented by

A

number of levels of each factor

38
Q

Cell means

A

Means within the cell

39
Q

Marginal means

A

Means below each column and to the right of each row

SRM (20 decks)

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