Nargis present new 1
Prepare by M. Noaman Akbar
Published on: Mar 3, 2016
Transcripts - Nargis present new 1
Significance of t-test
What is t-test
Who invented t-test
What kind of t is it
What is t-test of significance
Why we use t-test
When we use t-test
Examples and Explanation.
Applications of t-test
What is t-test ?
“A t-test is used to determine
whether a set or sets of scores are
from the same population.”
A t-test is any statistical hypothesis
test in which the test statistic follows
a Student's t-distribution if the null
hypothesis is supported.
Who invented t-test?
The t-test is 107 years old.
The t statistic was introduced
by William Sealy Gosset
Gosset published the t test in
Biometrika in 1908, but was
forced to use a pen name by his
employer who regarded the fact
that they were using statistics as
a trade secret. Hence, the
name Student's t-test.
What kind of t is it ?
Single sample t – we have only 1 group; want
to test against a hypothetical mean.
Independent samples t – we have 2 means, 2
groups; no relation between groups, e.g.,
people randomly assigned to a single group.
Dependent t – we have two means. Either
same people in both groups, or people are
related, e.g., husband-wife, left hand-right
hand, hospital patient and visitor.
significance of t-test ?
A t-test’s statistical
significance indicates whether
or not the difference between
two groups’ averages most
likely reflects a “real”
difference in the population
from which the groups were
Why we use t-test ?
A test of whether the slope of
a regressionline differs significantly
When we use t-test ?
An independent samples t-test is used
when you want to compare the means
of a normally distributed interval
dependent variable for two
independent groups. For example,
using the hsb2 data file, say we wish
to test whether the mean for write is
the same for males and females.
If we are analysing the heights of pine trees growing in two
different locations, a suitable null hypothesis would be that
there is no difference in height between the two locations. The
student's t-test will tell us if the data are consistent with this
or depart significantly from this expectation. [NB: the null
hypothesis is simply something to test against. We might
well expect a difference between trees growing in a cold,
windy location and those in a warm, protected location, but it
would be difficult to predict the scale of that difference -
twice as high? three times as high? So it is sensible to have a
null hypothesis of "no difference" and then to see if the data
depart from this.
List the data for sample (or treatment) 1.
List the data for sample (or treatment) 2.
Record the number (n) of replicates for each sample (the number
of replicates for sample 1 being termed n1 and the number for
sample 2 being termed n2)
Calculate mean of each sample
Calculate s 2 for each sample; call these s 1
2 and s 2
2 [Note that
actually we are using S2 as an estimate of s 2 in each case]
. Calculate the variance of the difference between the two means
(sd2) as follows
Calculate sd (the square root of sd
Calculate the t value as follows:
Enter the t-table at (n1 + n2 -2) degrees of freedom;
choose the level of significance required
(normally p = 0.05) and read the tabulated t value.
To compare the mean of a sample with
To compare the mean of one sample with
the mean of another independent
To compare between the value (reading)
of one sample but in two occasions.