Stats

Question 1

Standard deviation formula

Answer 1

sigma = sqrt[sum(x-xbar)^2/n-1]

Where n-1 = degrees of freedom

Question 2

Standard deviation

Answer 2

Square root of the variance

Question 3

T-tests

Answer 3

Compare 2 means to see if they are different from one another

Question 4

Types of t-test

Answer 4

One-sample t-test
Two-sample t-test (unpaired, independent samples)
Paired-samples t-test (dependent samples, repeated measurements)

Question 5

One-sample t-test

Answer 5

Tests the mean of a single group against a known mean

Question 6

Two-sample t-test

Answer 6

Compares the means from 2 separate sets of independent and identically distributed samples from 2 populations

Question 7

Paired-samples t-test

Answer 7

Compares means from the same group at different times

Used for comparing 2 measurements on the same item/person/thing

Question 8

Welch’s t-test

Answer 8

An adaptation of Student’s t-test that is more reliable when the samples have unequal variances/unequal sample sizes
Still maintains the assumption of normality
Can be generalised to more than 2 samples which is more robust than ANOVA

Question 9

Assumptions of a t-test

Answer 9

Data normally distributed/symmetrical
Data from multiple groups have the same variance
Data must be numeric and continuous
Data are independent (i.e. the data collection process is random)

Question 10

How to calculate if data from multiple groups have the same variance

Answer 10

Take the lowest and highest standard deviation values - if the highest standard deviation is less than twice the lowest standard deviation, the variance can be said to be the same

Question 11

Type I error

Answer 11

Concluding there is a difference when there isn’t

i.e. incorrectly rejecting the null hypothesis

Question 12

Type II error

Answer 12

Concluding there isn’t a difference when there is

i.e. incorrectly accepting the null hypothesis

Question 13

Family error rate

Answer 13

alpha
The probability that a test consisting of more than one comparison will incorrectly conclude that at least one of the observed differences is significantly different from the null hypothesis
Increases with each comparison

Question 14

Non-parametric tests

Answer 14

Used when the data does not fit a normal distribution
Can be used for ranked data
Much wider applicability than parametric tests because they make fewer assumptions - this also means they are more robust - but they do have less power in cases where a parametric test would be more appropriate
BUT parametric tests can never be applied to data that is obviously non-parametric

Question 15

Mann-Whitney U-test

Answer 15

= Wilcoxon rank-sum test
= non-parametric equivalent of the independent 2-samples t-test
Compares differences between 2 independent samples when the dependent variable is either ranked/ordinal, or is continuous but not normally distributed
Only valid for 2 groups
Can correct from multiple comparisons (family error rate)

Question 16

Wilcoxon signed-rank test

Answer 16

= non-parametric equivalent of the paired-samples t-test
Used to compared 2 related/matched/dependent samples / repeated measurements on a single sample
Uses ordinal/ranked data

Question 17

Spearman’s rank correlation coefficient

Answer 17

= non-parametric version of Pearson’s
= non-parametric test that measures the strength and direction of association between 2 ranked variables
i.e. measures the correlation
Data is ranked

Question 18

One-way ANOVA

Answer 18

A technique for comparing the means of 3 or more groups of data

Question 19

One-way ANOVA null hypothesis

Answer 19

Samples in all groups are drawn from populations with the same mean

Question 20

F-statistic

Answer 20

Produced from one-way ANOVA
Calculated by dividing the variance of the means between the groups by the variance within the groups
If the group means are from populations with the same mean values, the variance between the group means should be lower than the variance of the samples, following the central limit theorem

Question 21

When is F large?

Answer 21

When there is a larger difference between groups but little variance within groups
Larger F = probability that H0 is true decreases

Question 22

Assumptions of ANOVA

Answer 22

Same as those for other parametric tests

Question 23

Two-way ANOVA

Answer 23

A technique for comparing the means of 3 or more groups of data where 2 independent variables are considered
Can assess the effect of each independent variable on the dependent variable as well as if there is any interaction between the 2 independent variables

Question 24

Repeated measures ANOVA

Answer 24

Equivalent of the one-way ANOVA but for related rather than independent groups
An extension of the paired-samples t-test
Detects ant overall difference between related means
Also called ‘within-subjects ANOVA’ / ‘ANOVA for correlated samples’

Question 25

Kruskal-Wallis

Answer 25

= non-parametric equivalent of the one-way ANOVA
(also called ‘one-way ANOVA on ranks’ because it is a rank-based test)
Avoids assumption violations because non-parametric
Can compare 2 or more independent samples of equal or different sample sizes
Null hypothesis assumes the samples are form identical populations
Considered an extension of the Mann-Whitney U-test

Question 26

Tukey’s test

Answer 26

Post-hoc test for ANOVA
i.e. if you have run an ANOVA and found significant results, you can run a Tukey’s test to find out which specific groups’ means are different
Protects from false positives
Same assumptions as those for parametric tests
An extension fo the t-test to multiple group comparisons

Question 27

Dunnett’s correction

Answer 27

Post-hoc test for ANOVA
Similar to Tukey’s, except where Tukey’s compares every mean to every other mean, Dunnett’s compares every mean to a control test
Should only be used if there is a control group (if there isn’t, use Tukey’s)
Acts in a similar way to a t-test because it compares 2 groups

Question 28

Bonferroni correction

Answer 28

Post-hoc correction
Limits the possibility of getting a statistically significant result when testing multiple hypotheses
Used when performing many dependent or independent statistical tests at the same time (when performing many simultaneous test, the probability of a significant result increases with each test run)
Sets the significance cut off at alpha/n, i.e. if you run 20 simultaneous tests at alpha=0.05, the correction would be 0.0025
Suffers from a loss of power - i.e. it sometimes over-corrects for type I errors, leading to type II tests

Question 29

SNK method

Answer 29

= Newman-Keuls / Student-Newman-Keuls method
Post-hoc test
Again used to identify sample means that have been shown to be significantly different from one another following an ANOVA
Very similar to Tukey’s but uses different critical values
More like to commit type I errors than Tukey’s test (more powerful but less conservative than Tukey’s)

Question 30

What does the ‘power’ of a statistical test refer to?

Answer 30

The probability that the test will reject a null hypothesis