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EPI PR3144 > LEC 5 Parametric Tests ll > Flashcards

LEC 5 Parametric Tests ll Flashcards

1
Q

Parametric tests for >2 groups

  • independent
  • related
A
  1. one-way ANOVA (independent)

2. repeated measure ANOVA (related)

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2
Q

One-way ANOVA assumptions (4)

A
  1. the samples are random samples of their population
  2. the underlying populations are normally distributed
  3. the underlying populations are independent
  4. the underlying populations have equal variances
    - unequal variances (Welch ANOVA)
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3
Q

Why do we need to use one-way ANOVA instead of conducting all possible independent-samples t-tests?

A

To control the overall probability of making a Type l error on the pre-determined significance level (alpha=0.05)

Type 1 error : false +ve (results say have association but in reality no association)

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4
Q

Type l error

A

= 1 - alpha

  • alpha = 0.05
  • false positive
  • reject null hypothesis when null hypothesis is true
  • in reality there is no statistically significant difference but results show statistically significant difference
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5
Q

Type ll error

A
  • beta
  • false negative
  • failure to reject null hypothesis when alternative hypothesis is true
  • in reality there is statistically significant difference but results show no statistically significant difference
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6
Q

2 sources of variation

A
  1. within groups (SD)

2. between groups (mean compared to overall mean)

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7
Q

Within group variation

A
  • variation of individual values around their population means
  • SD
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8
Q

Between groups variation

A
  • variation of population means around the overall mean
  • one way ANOVA will yield p<0.05
  • hence do post-hoc test to determine where is the difference in population means
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9
Q

Overall mean

A

Summation of all scores / entire population

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10
Q

One-way ANOVA hypothesis

A

Null hypothesis
- all the means of the underlying populations are the same

Alternate hypothesis
- not all the means of the underlying populations are the same
OR
- the means of at least 2 of the underlying populations are different

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11
Q

Tests of normality

A
  1. Shapiro-Wilk (n<50)

2. Kolmogorov-Smirnov (n>=50)

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12
Q

Normality test hypothesis

A

Null hypothesis
- the underlying population follows normal distribution

Alternate hypothesis
- the underlying population does not follow normal distribution

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13
Q

Tests of equal variance

A
  1. F test
    - 2 independent groups
    - normal distribution
  2. Levene’s test
    - at least 2 independent groups
    - normal or non-normal distribution
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14
Q

Levene’s Test hypothesis

A

Null hypothesis
- the underlying populations have equal variances

Alternate hypothesis
- NOT ALL underlying populations have equal variances

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15
Q

If one-way ANOVA test shows significant difference, what other test to do?

A

Post-hoc test

To determine where the difference lies

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16
Q

Post-hoc test (2)

A
  • identify the differences while controlling the overall probability of making type l error (alpha)
  • involve testing each pair of means individually
17
Q

More conservative post-hoc test (3)

A
  • means a larger diff is required to show significance in the test
  • reduces statistical power (1-beta) and thus higher chance for type ll error (beta)
  • allows the control of type l error

type l error : false +ve
type ll error : false -ve

18
Q

Types of post-hoc tests (5)

A
  1. Bonferroni adjustment
  2. Least Significant Difference (LSD) test
  3. Tukey’s test
  4. Scheffe’s procedure
  5. Dunnett’s test
19
Q

Bonferroni adjustment (3)

A
  • very conservative
  • for any type of statistical tests (parametric & non-parametric)
  • adjusted significance level = (alpha/m)
    m = number of pairwise comparisons
20
Q

LSD (3)

A
  • least conservative
  • hence higher chance of type l error (false +ve) & show more statistical significance
  • strongly discourage to use it

false +ve : rejecting Ho when Ho is true

21
Q

Tukey’s test

A
  • more conservative than LSD
22
Q

Scheffe’s procedure

A
  • most conservative
23
Q

Dunnett’s test

A
  • to compare against control group
24
Q

Repeated measures ANOVA

A

to compare >2 paired groups

eg same group of subjects over different conditions

25
Q

Repeated measures ANOVA hypothesis

A

Null hypothesis
- the means of the underlying populations are equal

Alternate hypothesis
- not all the means of the underlying populations are equal
OR
- the means of at least 2 populations are different

26
Q

Relationship between LSD and Bonferroni test

A

Bonferroni p-value = m x (LSD’s p-value)

cos Bonferroni adjustment is alpha/m & LSD does not adjust for alpha value

27
Q

Types of pairing in paired groups

A
  1. Self pairing
    - self control
  2. Matching
    - similar characteristics/baselines are compared
28
Q

Adjusted significance level (Bonferroni adjustment)

A

= alpha/m

m is the number of comparison group/pairwise group

29
Q

ANOVA

A

Analysis of Variance

30
Q

Statistical test for :

  • > 2 independent groups
  • continuous normally distributed
  • equal variance
A

One-way ANOVA

31
Q

Statistical test for :

  • > 2 independent groups
  • continuous normally distributed
  • unequal variance
A

Welch-ANOVA

32
Q

When using statistical software to compute p-values for post-hoc analysis, do you take into consideration bonferroni’s adjusted significance level or p=0.05?

A

Depends

  • cos software might readjust p-value back to 0.05 level
  • check footnote for the significance level
33
Q

p<0.05 for one-way ANOVA

A
  • suggests between group variability

- cos assumption of one-way ANOVA is equal variance within sample groups

EPI PR3144 (24 decks)

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