Week 16 Flashcards
What is the difference between parametric and non-parametric statistical tests?
Parametric (may be used) = Population is normally distributed
Nonparametric (have to be used) = Not normally distributed population or no assumption can be made about the population distribution
What are the two main groups of statistical tests?
Parametric
Non-parametric
What are parametric tests?
- Compare means and variances
- Only used when data follows normal distribution
- Can test data against the hypothesis that they are consistent with normally distributed data (eg Shapiro-Wilk and olmogorov Smirnov)
What are t-tests comparisons between…?
Comparisons between 2 sample means (or one sample mean and one known population mean)
What are ANOVA used for?
To test hypothesis that multiple samples come from same population by comparing variation within each sample and variance between each sample
(useful when comparing multiple variables)
What are the most commonly used parametric tests?
T-tests
ANOVA
T-tests (AKA student’s t-test) are used to compare what type of data distribution?
Normally distributed data with similar standard deviations (typically used to compare one or two samples)
T-tests test the probability that….
the samples come from a single population with single mean
(work well with smaller samples (n~30)
What is a two-tailed test?
(When trying to reject a null hypothesis: there are 2 possibilities. We reject because the mean value of one sample is higher than that of the other sample or it is lower)
If we allow the null hypothesis (H0) to be rejected from either direction (higher or lower) – we are rejecting when the result is in either tail of the test distribution – this is a two tailed test!.
What is a one-tailed testt?
(When trying to reject a null hypothesis: there are 2 possibilities. We reject because the mean value of one sample is higher than that of the other sample or it is lower)
If we know that a measurement in a population is larger (or smaller) than another, then we know that the residual 5% will be in the upper (or lower) tail of the normal distribution.
So for a one-tailed test we reject null hypothesis only when result is in a single tail of the test distribution
What are the three different types of t-tests?
One sample t-test
Paired samples t-test
Independent samples t-test
When is a one sample t-test used?
When we have a single sample and want to compare the mean of that sample with a fixed value (usually a population mean or estimated population mean), we use a One Sample t-test
When is a paired sample t-test used?
Where two observations are made on the same sample subjects, we need the paired samples t-test.
When is an independent samples t-test used?
Were we have two samples and have measured the variable on each of them.
What do t-tests calculate?
A t-value (number of standard errors that sample mean is away from the population mean
Formula for a one-sample t-test?
t = X bar - E / SEM
E (Fixed value)
SEM (Standard error of the mean)
X bar (sample mean)
What is the paired-sample t-tests?
- Compares means of variable in same sample under different conditions, or at two different times
- Calculated by dividing mean of differences between each pair by the standard error of the difference
Formula for a paired-sample t-test?
t = D bar / SEd
D bar (mean difference between each pair)
SEd (standard error of differences)
What is ANOVA?
a statistical test that is used to compare multiple samples (to be more accurate – multiple sample means)
This is a powerful statistical technique that can be used to compare e.g. multiple samples, from multiple groups, under the influence of multiple factors.
ANOVA vs T-test?
- use a t-test for each individual comparison, ANOVA uses a single but it covers all comparisons
- ANOVA also has the added benefit of being able to consider the effect of multiple factors on a variable of interest.
- the more t-tests we do the greater the chance of coming to the wrong conclusion.
ANOVA tests compare what?
the variability between samples with the variability within samples.
What are the two types of ANOVA tests?
One-way ANOVA (compare means from more than two samples)
Repeated-measures ANOVA: (Used when there are repeated measurements on the same sampling unit. ) - each subject appears in each group
When would you run a post-hoc test when using ANOVA? Examples?
ANOVA tells us whether there is a significant difference between samples but it doesn’t tell us which of those samples have that difference. So post-hoc tests are used
EG: Tukey, Bonferroni correction, Dunnett’s, Scheffe
Unpaired t-test used to compare? is calculates by?
Used to compare means of the same variable in two different samples
Calculated by dividing the difference between each of the means of the two samples by the standard error of the difference
Formula for unpaired t-test?
t = X bar a - X bar b / SEd
Xbar a and X bar b (meas of two samples)
SEd (standard error of differences
What is independent-samples t-test also known as?
Unpaired t-test
