Stats Flashcards
Standard deviation formula
sigma = sqrt[sum(x-xbar)^2/n-1]
Where n-1 = degrees of freedom
Standard deviation
Square root of the variance
T-tests
Compare 2 means to see if they are different from one another
Types of t-test
One-sample t-test
Two-sample t-test (unpaired, independent samples)
Paired-samples t-test (dependent samples, repeated measurements)
One-sample t-test
Tests the mean of a single group against a known mean
Two-sample t-test
Compares the means from 2 separate sets of independent and identically distributed samples from 2 populations
Paired-samples t-test
Compares means from the same group at different times
Used for comparing 2 measurements on the same item/person/thing
Welch’s t-test
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
Assumptions of a t-test
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)
How to calculate if data from multiple groups have the same variance
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
Type I error
Concluding there is a difference when there isn’t
i.e. incorrectly rejecting the null hypothesis
Type II error
Concluding there isn’t a difference when there is
i.e. incorrectly accepting the null hypothesis
Family error rate
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
Non-parametric tests
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
Mann-Whitney U-test
= 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)
Wilcoxon signed-rank test
= 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
Spearman’s rank correlation coefficient
= 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
One-way ANOVA
A technique for comparing the means of 3 or more groups of data
One-way ANOVA null hypothesis
Samples in all groups are drawn from populations with the same mean
F-statistic
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
When is F large?
When there is a larger difference between groups but little variance within groups
Larger F = probability that H0 is true decreases
Assumptions of ANOVA
Same as those for other parametric tests
Two-way ANOVA
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
Repeated measures ANOVA
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’
