Section 5 (p59 - 68) Flashcards
When is student’s t distribution used?
Population standard deviation is unknown
Population is normally distributed
Independent items
What is the parameter of student’s T distribution?
Number of degrees of freedom
What does the degrees of freedom equal?
n-1
What does the standard error equal for student’s t distribution?
s/ square root of n
How many t distributions are there?
An infinite number
What happens, in terms of the normal and the t distribution, as the size of the sample increase?
t distribution approximates the normal more closely
What does the critical values depend on in the t distribution?
The sample size and significance level
Where can critical values for the t distribution be found?
Tables or the internet
In practice, what test statistic is used to test means?
t
What type of t-test is done when you are comparing a hypothesis about a population mean with unknown standard deviation against a reference?
One-sample T-test
What is the symbol for the critical value at the c% confidence level for the t distribution with n-1 degrees of freedom?
tn-1,c e.g. t19,0.99
What are the 3 types of t-tests?
One-sample
Paired/ dependent
Un-paired/ independent
How does a one-sample T test differ from a test when the population standard deviation is known?
Instead of using the z statistic with set critical values for the confidence interval, the t statistic is used and critical values are determined from the probability distribution function
What is another name for dependent observations?
Paired observations
Name for type of observation when repeated observations are made on the same individuals?
Dependent
Name for type of observation when treatment is applied to different individuals?
Independent
What is the principal source of variation of response to a treatment?
Between-subject differences
How can between-subject differences be eliminated entirely?
By applying both treatments to the same individual
How can between-subject differences be reduced?
By matching for factors known to affect the outcome
In trials where matching of factors known to affect outcomes occurs, are the outcomes dependent or independent?
Dependent
Other name for a dependent T test?
Paired T test
In comparison of dependent continuous data distributions, what are inferences based on?
The mean difference
Symbol for the mean difference?
d with a line above it
Can inferences using the mean difference be based on the t distribution?
Yes, providing the differences are plausibly normally distributed
What is a hypothesis test of the equality of 2 independent sample means normally doing?
Testing if the samples have been drawn from the same (plausibly normal) population
How can an estimate of the variance of the population be obtained for an independent t test?
When the sample variances are comparable (not significantly different) they can be pooled
Should you still do an independent t test if the sample variances are not comparable?
Exercise caution doing this as clearly the samples are not drawn from the same population
What are the 4 options when considering doing an unpaired T test if the sample variances are not comparable?
Investigate the relationship between means and variances (use a logarithmic transformation)
Use Welch’s modified T test
Use a non-parametric test to compare the means
Do not proceed with the test of the means
Why does a logarithmic transformation sometimes help achieve equality of variances for an unpaired T test?
In some cases, the variability of a measurement increases with magnitude
Name the approximation to a t test when samples are known to have arisen from normal distributions with unequal variances?
Welch’s test
What distribution is formal tests of the equality of two variances based on?
The F distribution
What is the f statistic equal to?
s1 squared / s2 squared
What are the 2 parameters of the f statistic?
n1 - 1 and n2- 1
How do you decide which variance is s1 squared and which is s2 squared for the f statistic?
s1 squared is the larger variance
How are the results of the f statistic interpreted?
Significance of the f statistic can be established from tables
If F is not significant, the variances are comparable and population variance can be calculated
What does the 95% confidence interval for the differences between the sample means equal?
Observed difference between means +/- tn1+n2-2 X standard error of difference (get these equations from test statistic of independent t-test)
