The Paired Samples t Test
compares the means of two measurements taken from the same individual, object, or related units
. These “paired” measurements can represent things like: A measurement taken at two different times (e.g., pre-test and post-test score with an intervention administered between the two time points)
What is a paired t-test good for?
A paired t-test is used
when we are interested in the difference between two variables for the same subject
. Often the two variables are separated by time. … Since we are ultimately concerned with the difference between two measures in one sample, the paired t-test reduces to the one sample t-test.
What does a paired t-test tell you?
The paired sample t-test, sometimes called the dependent sample t-test, is a statistical procedure used to
determine whether the mean difference between two sets of observations is zero
. In a paired sample t-test, each subject or entity is measured twice, resulting in pairs of observations.
What do unpaired t tests show?
What is an unpaired t-test? An unpaired t-test (also known as an independent t-test) is
a statistical procedure that compares the averages/means of two independent or unrelated groups to determine if there is a significant difference between the two.
What does the t-test reveal?
The t test tells
you how significant the differences between groups are
; In other words it lets you know if those differences (measured in means) could have happened by chance.
How do you interpret paired t-test results?
- Step 1: Determine a confidence interval for the population mean difference. First, consider the mean difference, and then examine the confidence interval. …
- Step 2: Determine whether the difference is statistically significant. …
- Step 3: Check your data for problems.
How do you know if data is paired?
Two data sets are “paired” when the
following one-to-one relationship exists between values in the two data sets
. Each data set has the same number of data points. Each data point in one data set is related to one, and only one, data point in the other data set.
What is the difference between t test and paired t test?
Two-sample t-test is used when the data of two samples are statistically independent, while the paired t-test is used when data is
in the form of matched pairs
.
Is there a paired Z test?
The paired z-test may be
used to test whether the mean difference of two populations is greater than, less than, or not equal to 0
. Because the standard normal distribution is used to calculate critical values for the test, this test is often called the paired z-test.
What is the formula for paired t-test?
Paired T-Test Formula
The formula of the paired t-test is defined as
the sum of the differences of each pair divided by the square root of n times the sum of the differences squared minus the sum of the squared differences, overall n-1
. Where, Σd is the sum of the differences.
What is the difference between a t-test and an Anova?
The Student’s t test is used to compare the
means between two groups
, whereas ANOVA is used to compare the means among three or more groups. … A significant P value of the ANOVA test indicates for at least one pair, between which the mean difference was statistically significant.
What are the assumptions of a paired t-test?
Paired t-test assumptions
Subjects
must be independent
. Measurements for one subject do not affect measurements for any other subject. Each of the paired measurements must be obtained from the same subject. For example, the before-and-after weight for a smoker in the example above must be from the same person.
What does p-value tell you?
A p-value is
a measure of the probability that an observed difference could have occurred just by random chance
. The lower the p-value, the greater the statistical significance of the observed difference. P-value can be used as an alternative to or in addition to pre-selected confidence levels for hypothesis testing.
How do you reject the null hypothesis in t-test?
If the
absolute value of the t-value is greater than the critical value
, you reject the null hypothesis. If the absolute value of the t-value is less than the critical value, you fail to reject the null hypothesis.
When should you use the Z test?
The z-test is best used for
greater-than-30 samples
because, under the central limit theorem, as the number of samples gets larger, the samples are considered to be approximately normally distributed. When conducting a z-test, the null and alternative hypotheses, alpha and z-score should be stated.
