Hypothesis Tests: The t-Tests Flashcards
What is a t-test
A statistical test that COMPARES THE MEANS OF TWO SAMPLES
What is the Null Hypothesis?
The hypothesis that assumes the POPULATIONS ARE IDENTICAL
If P<0.05
The results is against the null hypothesis
If P<0.01
Strong evidence the result is against the null hypothesis
If P<0.001
Very strong evidence the result is against the null hypothesis
If the null hypothesis is true what is the P value
P>0.05
What are the types of T-test
Unpaired and paired
How is the differences in data structure of the two data sets within the t-tests reflected
Reflected in the SE
What does a unpaired t test do
Compares two UNRELATED SAMPLES
such as a group of patients given saline or fentanyl
What assumptions are there with an unpaired t test?
- Each sample is drawn from a NORMAL POPULATION
- POPULATIONS HAVE A COMMON STANDARD DEVIATION
What is the null hypothesis for a unpaired t-test
The population means are the same
Can you still do a unpaired t-test when the populations are NON-NORMAL but departure from NORMALITY is SLIGHT
Yes as the violations of the ASSUMPTIONS are usually of little consequences
What does SDs being not equal relate to
The data being skewed
What is normal distribution characterised by
Standard Deviation and Mean
Therefore a test that assessed equality of means and pay no attention to the standard deviation. Therefore the best estimate of population mean draws on information from both samples and is a pooled estimate
What is a paired t test
Compares TWO RELATED SAMPLES
What does the Paired t test take into account
The pairing by FORMING THE DIFFERENCES BETWEEN EACH PAIR. Once the differences have been formed the original observations are discarded.
What does the paired t test anaylse
ONLY THE DIFFERENCES BETWEEN EACH PAIR
How to assess whether a SINGLE SAMPLE OF DIFFERENCES COMES FROM A POPULATION WITH MEAN ZERO
Paired t-test
What is SE in an unpaired t test based on
Standard deviation which measures the VARIATION BETWEEN the two samples
In a paired t test the act of taking the difference between two values from related samples would it expectedly remove
It removes the variation of standard error between the two samples from the data
What will pairing the data in the lead to in a paired data
A more sensitive experiment
How will the advantage of pairing the data be lost
If it is not reflected in the arithmetic used for the data analysis
How will the correct precision be ascribed to the difference in means in a t test
The correct precision can only be ascribed of the APPROPRIATE SE for the paired data is used
What is the Assumption in Paired t test
1.DIFFERENCES between the two related samples have to come from a NORMAL DISTRIBUTION.
(Normality not necessary to specify the distribution of the individual observations , just there Differences)
- MODEST departures from normality are not usually troublesome, like unpaired
If 0 is included in a 95% confidence interval for the t-test what will the associated hypothesis test give
P>0.05
If 0 is NOT included in a 95% confidence interval for the t-test what will the associated hypothesis test give
P <0.05
If the null hypothesis (P>0.05) is TRUE where are the values in relation to the 95% confidence intervals
The values are within the 90
5 confidence interval are the values of X that are compatible with the data
In a Paired test what does it not assume
- 2 Populations
2, Normality in each populations
In a paired test what does it assume
The differences are normally distributed
In a unpaired t test what does it assume
- The two populations are normal
2, Has a common standard deviation but does not assume eqaulity of SD estimates from the two samples
