T- TESTING
Mohith
Bhagyavalli
Rajasri
Kartik
AGENDA
What is T-testing
Why we use
When to use
Comparison between Z & T
tests
Advantages
Real time Example
Conclusion
T- Testing is Hypothesis Test statistics.
T- Testing, is also known as T- value and it is used to determine significance
difference between the means of two groups.
The two groups could be, for example, patients who received drug A once
and drug B once, and you want to know if there is a difference in blood pressure
between these two groups
T-Test
formula
Where,
‘x’ bar is the mean of the sample
‘μ’ is population mean
‘σ’ is standard deviation
‘n’ is the number of observations
TYPES OF T-TESTS
There are three different types of t-tests. The one sample t-test, the independent-sample t-
test and the paired-sample t-test.
ONE SAMPLE T-TEST:
When do we use the one sample t-test (simple t-test)? We use the one sample t-
test
when we want to compare the mean of a sample with a known reference mean
Eg : A manufacturer of chocolate bars claims that its chocolate bars weigh 50 grams on
average. To verify this, a sample of 30 bars is taken and weighed. The mean value of this
sample is 48 grams
We can now perform a one sample t-test to see if the mean of 48 grams is significantly different from the claimed 50
grams.
INDEPENDENT SAMPLE T-
TEST
We use the t-test for independent samples when we want to compare the means
of two independent groups or samples. We want to know if there is a significant
difference between these means.
We would like to compare the effectiveness of two painkillers, drug A and drug
B
To do this, we randomly divide 60 test subjects into two groups. The first
group receives drug A, the second group receives drug B. With an
independent t-test we can now test whether there is a significant difference in
pain relief between the two drugs.
PAIRED SAMPLE T-TEST
The t-test for dependent samples is used to compare the means of two
dependent groups.
We want to know how effective a diet is. To do this, we weigh 30
people before the diet and exactly the same people after the diet.
Now we can see for each person how big the weight difference is
between before and after. With a dependent t-test we can now check
whether there is a significant difference.
Comparison between Z-test and T- test
Z-TEST:
• Data size is Greater then 30 (>30)
• Data was randomly selected from a broader population
• Sample sizes should be equal if possible
• Data is distributed normally (if data size >30)
T-TEST
• Data size is smaller than 30 (<30)
• Data wasn’t randomly selected
• Sample sizes are not equal
• Data is not Normally Distributed
Advantage of T-test compared to Z-
test
The Student t-test is a handy statistical tool with several advantages for
different research situations. Some of the main advantages are:
• Works with Different Sample Sizes: Unlike other tests, the t-test is flexible
and can be used with both small and large samples.
• Versatile Application: The test finds use in diverse fields like medical
research, education studies, market research, and engineering, showcasing
its wide-ranging applicability.
• Easy to Calculate: This test is relatively simple and straightforward to
calculate. This simplicity makes it practical and applicable in various
research scenarios.
What is P-value
P-value or Probability value is probability of obtaining test results at least as
extreme as the observed
Results, assuming that the null hypothesis is true. It quantifies the evidence
against null hypothesis
Determine P-value in Excel
Here, array1 refers to the first set of data , array2 is the second set of data
, tails refers to whether you want to run a one- or two tailed test, and the
type refers to: 1 = paired test 2 = two sample equal variance test 3 = two
sample unequal variance test The value returned from this formula is
your p-value
P_value =TTEST(array1, array2,tails,type)
CONCLUSION
If your calculated p value is greater than the significance p-value,
you can conclude that the difference between the means for the two
groups is Not significantly different. We accept the null hypothesis
and conclude that the alternative hypothesis is correct.
If your calculated p value is lower than the significance p-value,
you can conclude that the difference between the means for the two
groups is significantly different. We reject the null hypothesis.
