Comparing Two Groups Flashcards
How do you compare two unrelated groups (apples and oranges)?
By comparing their z score (standard deviation)
What test do you use to compare your data against a theoretically predicted mean?
One sample t-test
In one-sample t-tests, what do these symbols mean?
X = The sample mean we actually observed
μ = true population mean if the null hypothesis is correct
In one-sample t-tests, what does σ mean?
SEM (standard error of the mean)
What is the R code for one-sample t-tests?
t.test(x, y)
x = the variable containing raw data
y = true population mean, according to null hypothesis
alternative: oneSampleTTest(x, y)
What is the symbol for the test statistic in a one-sample t-test?
t
Since one-sample t-tests are unsure about what the true standard deviation is, how do they obtain the overall sampling distribution for the t-statistic?
Average over lots of possible choices for the standard deviation.
What happens to the sampling distribution of t as the sample size (N) grows larger?
Our estimate of the standard deviation is more precise and the t-distribution grows similar to normal.
How are degrees of freedom calculated for a t-distribution?
N-1
N = number of data points
1 = number of constraints (i.e. the mean)
How is the t-tests t statistic calculated
(Sample mean we observed - true population mean if the null hypothesis is correct)
/ (divided by)
(The true population standard deviation / SEM)
Because the width of the t distribution depends on sample size, the size of the rejection region changes as ___ increases
N
(number of data points)
What is Cohen’s d?
A simple measure of effect size
How do you interpret Cohen’s d (roughly)
How do you run Cohen’s d in R?
library(lsr)
>cohensD(x, y)
(x,y same as t-test)
How do you write up the results of a one-sided t-test
e.g. (t(19) = 3.42, p = .003)
How do you write the null hypothesis and the alternative hypothesis for one-sided and two-sided one-sample t-tests?
Two-sided one-sample t-test:
H0: the true mean is (x)
H1: the true mean isn’t (x)
One-sided one sample t-test:
H0: the true mean is x or less (or more if the other way)
H1: the true mean is above x
What is the R command for one-sided t-tests in R?
t.test(x, y, alternative=”greater”)
x = sample mean
y = theorised mean
alternative = ‘greater’ or ‘less’ depending on direction
When do you use an independent samples t-test?
When comparing two groups
How do you write the null hypothesis and alternative hypothesis for independent samples t-tests?
What assumptions are made in an independent samples t-test?
population distributions are normal
observations are independently sampled
groups have the same standard deviation
(a.k.a. “homogeneity of variance”, “homoscedasticity”)
What is the diagnostic test statistic for independent samples t-tests?
What is the sampling distribution?
test statistic: t
Sampling distribution: t, with N1+N2-2 degrees of freedom
If the null hypothesis is true in an independent sample t-test, what should the sampling distribution of t be?
Close to 0
If different, substantially different from 0
Student t-test assumes what about variance?
Equal variance
What is the R command for a student t-test?
t.test( price ~ colour, wines, var.equal=TRUE )
just like independent samples but with added variance
What is the R command for an independent samples t-test?
independentSamplesTTest( x ~ y, z )
x ~ y are groups comparing
z is data set
The Welch t-test assumes what about variance?
Not equal variance
(much safer thing to do)
How does the Welch t-test adjust for not having equal variance?
“Effective” degrees of freedom is adjusted to be a bit smaller, depending on just how unequal the sample standard deviations are (not necessarily a whole number)
R command for Welch t-test?
t.test (price~colour, wines)
- Price~colour = the formula that describes our test, to see if price is related to colour*
- Wines = the dataset that the formula is taken from*
What are the important test results to report for a Welch t-test?
The test statistic, degrees of freedom, p-value, effect size and confidence interval (for the difference between means)
What is the command in R for a one-sided two-sample t-test?
t.test(price ~ colour, wines, alternative=”less”)
What is a z-score?
They reflect the distance from the mean in terms of standard deviations
e.g. z-score of +2 means it is 2 standard deviations above the mean
What does the test statistic (t) represent in t-tests?
Reflects the distance of your data from the mean
Define: homoscedasticity
Same variance
