statistics 1

univariate data

one measured variable

sex is a nominal variable or factor with (?) levels

2

bivariate data

two measured variables

one way ANOVA

• univariate data

• one factor with many levels

are nominal variables controlled by the experimenter?

no

two way ANOVA

• one measured variable

• two factors with many levels

• number of factors = number of controlled variables

how is the number of groups calculated in two way ANOVA?

number of levels in factor 1 x number of levels in factor 2

groups and levels are interchangeable terms in a (?) ANOVA

one-way

how many groups in this two way ANOVA

factor 1 = disease (control vs obstructive) = 2 levels

factor 2 = dose = 5 levels

2 × 5 = 10 groups

t-test is used to measure univariate data with:

1 factor and 2 levels

one way ANOVA is used to measure univariate data with:

1 factor and many levels

two way ANOVA is used to measure univariate data with:

1 factor and many levels

paired t-test vs unpaired t-test

• paired → uses same group of participants

• unpaired → uses different groups of participants (independent)

what are the two types of unpaired t-tests?

Student’s and Welch’s

what are the two types of one way ANOVAs?

• independent samples → e.g. disease (diseased vs non diseased participants)

• repeated measures → e.g. dose (each participant receives each dose)

what are the three types of two way ANOVAs?

• independent samples → both factors

• repeated measures → both factors

• mixed design → one factor is independent samples, one is repeated measures

interaction

• no interaction → effect of factor 1 was same for all levels of factor 2

• interaction → effect of factor 1 was different between levels of factor 2

• if the graphs are parallel → no interaction

main effects

the effect of a controlled variable on the measured variable

robust test

• t-tests are very reliable

• won't give false positives or negatives

• results remain unaffected with minor data shifts

fragile test

• asssumptions must be rigorously applied

• results change easily with minor data shifts

• useless for repeated measures → minor deviations produce large errors

normal distribution

symmetric data pattern that is centered around an average value

both paired and unpaired t-test assumes (?) distribution

normal

paired t-tests are correlated: what does this mean?

describes the size and direction of a relationship between two or more variables

test for correlation (normal distribution)

Pearson’s r

student’s t-test

• unpaired t-test

• groups are independent

• assumes equal variance

what is the test for equal variance between two levels?

Fisher’s F test

welch’s t-test

• unpaired t-test

• groups are independent

• does not assume equal variance

independent samples ANOVA vs repeated measures ANOVA

• both normally distributed

• independent samples ANOVA → same variance between groups

• repeated measures ANOVA → constant sphericity

what is sphericity?

• correlation of all groups are identical

• differences between groups must have equal variance

what test’s assume normality? (list 5)

what is homoscedasticity?

assumption of equal variance

student’s t-test and independent sample ANOVA are (?) to deviations from homoscedasticity?

robust

repeated measures ANOVA assumes (?) and is (fragile/robust?)

• sphericity

• fragile to deviations from sphericity

• robust to deviations from normality

Greenhouse-Geisser epsilon is a measure of (?)

sphericity

compound symmetry

sphericity where all variances and covariances are the same

how to determine when to use non-parametric test

1. plot a frequency histogram

• indicator of skew and kurtosis

• skew → 0 normal

• kurtosis → 0 normal

2. test for normality

• e.g. Shapiro-Wilk test

• p<0.05 → not normal

3. normality plots

• data points should fall linearly

why is using parametric tests ok for when there are small abnormalities?

• ANOVA and t-tests are robust to deviations from normality

• independent samples ANOVA and unpaired t-tests assume all groups/levels are normal

• repeated measures ANOVA and paired t-test assume the differences are normal

non-parametric tests (parametric test equivalents)

non-parametric tests

• do not assume normal distribution

• assumes big differences in variance deviations

parametric tests use size, non-parametric tests use (?)

ranks

non-parametric tests use (? and ?) instead of mean and standard deviation

• median

• IQ (interquartile range)

when to use non-parametric tests (list 6)

semi-quantitative data

• uses non-parametric testing

• variable is ranked not quantitatively measured

summary

summary

define