This document summarizes a seminar on independent and paired t-tests. The t-test assesses whether the means of two groups are statistically different. An independent t-test is used to compare the means of two independent groups, while a paired t-test compares the means of the same variable measured at two different time points. Both tests calculate a critical t-value to compare to the calculated t-value to determine whether to reject the null hypothesis of no difference between the means. The document provides examples of performing independent and paired t-tests using formulas and the statistical software SPSS.

1. RAK college of Nursing
RAK Medical and Health Sciences University
Seminar on: T-test, independent and paired samples
Course: Statistics for health professionals
Prepared by:
Abdelrahman Alkilani- 15906012
Sultan Sultan- 15906013
Submitted to Dr. Maragatham Kannan, Associate professor
Date of submission: 15/11/2015

2. Objectives
By the end of this seminar, you’ll be able to:
 Define T-test
 Discuss the merits and demerits of t-test
 Identify the independent t-test and discuss
when to use it.
 Identify the paired t-test and discuss when to
use it.
 Use the correct formulas of t-test
 Use the t-test through SPSS

3. T-test
 The t-test assesses whether the means of
two groups are statistically different from
each other

4. Merits and demerits
 Merits:
– It reduces the possibility of guising the correct
answer .
– It covers greater amount of contents than
matching types test.
 Demerits
– it is only appropriate for questions that can be
answered by short responses
– There is a difficult in scoring when the questions
are not prepared properly and clearly

5. Independent t-test
 It is a parametric test used to determine if a
difference exists in the means of two groups
on a particular characteristic.

6. Independent t-test
 Used when:
– The grouping variables is dichotomous
– The variable measuring the characteristics of
interest is normally distributed.
– The variable measuring the characteristic of
interest in interval or ratio
– The measure of each value of the variable, which
measures the characteristic of interest, constitute
and independent random sample

7. Computing the independent t-test
 Need two t-values:
– Calculated t-value
– Critical t-value
 If calculated t-value is greater than critical t-
value, then reject the null hypothesis.

8. Computing the independent t-test
 Example:
In a study, we want to know whether smokers and
non-smokers have equal brain sizes.

9. n Non-smokers Smokers
1 7.3 4.2
2 6.5 4.0
3 5.2 2.6
4 6.3 4.9
5 7.0 4.4
6 5.9 4.4
7 5.2 5.5
8 5.0 5.1
9 4.7 5.1
10 5.7 3.2
11 5.7 3.9
12 3.3 3.2
13 5.0 4.9
14 4.6 4.3
15 4.8 4.8
16 3.8 2.4
17 4.6 5.5
18 5.5
19 3.7

10. Computing the independent t-test
1. State the null and alternative hypothesis.
H0 : There will be no difference in the means of the two
groups.
“smokers and non-smokers have equal brain size”
HA : smokers and non-smokers have unequal brain size

11. Computing the independent t-test

12. Computing the independent t-test

14. Computing the independent t-test
 As the calculated t-value (3.07) greater than
critical t-value (2.042), the null hypothesis
can be rejected.

15. Independent t-test using SPSS

16. Independent t-test using SPSS
1- check if it is normally distributed

17. A- Put the independent variables in the factor list
B- Put the dependent variable in the dependent list
C- Click on “Plots” and choose “histogram”

18. A- in the output window, double click on the histograms of the independent variables.
The choose the icon of curve

19. A- in the output window, double click on the histograms of the independent variables.
The choose the icon of curve

20. 2- Compare the means of the independent
variable

21. A- Put the independent variables as the grouping variables
B- Define the groups as entered in the SPSS.
E.g. Gender; Male=M, Female=F

22. -Sig = 0.679
-alpha= 0.05
-Sig > alpha. So, we will reject the null hypothesis

23. Paired t-test
 The measurements of the same variable at
two different points are compared.
 It can be measured at the same time on two
different people who are matched on some
condition (e.g. age, gender, twins).

24. Paired t-test
 Used when:
– There are two measurements of characteristic of
interest.
– The two measures that are compared are
normally distributed or at least 30 pairs.
– The measurement scale is either interval or ratio.

25. Computing the paired t-test
 Need two t-values:
– Calculated t-value
– Critical t-value
 If calculated t-value is greater than critical t-
value, then reject the null hypothesis.

26. Computing the paired t-test
Pre post Difference
(D)
Difference 2
1 7 6 36
2 6 4 16
1 8 7 49
Sum=17 Sum = 101

27. Computing the paired t-test

28. Computing the paired t-test

29. Computing the paired t-test
 Degree of freedom = n-1
= 2
Alpha = 0.05
Critical t from the t- table = 2.92

30. Computing the paired t-test
 Calculated t > critical t
 6.425 > 2.92
 We will reject the null hypothesis. So, there is
a difference between pre and post

31. Paired test using SPSS

32. 1- check the normal distribution the same as we did in the independent variables

33. 1- check the paired sample t-test

34. Paired test using SPSS
 As the sig. < alpha
0.023 <0.05
Null hypothesis will be accepted

35. Summary
 The t-test assesses whether the means of
two groups are statistically different from
each other
 Independent t- test is to determine if a
difference exists in the means of two groups
on a particular characteristic.
 Paired samples t-test is a measurements of
the same variable at two different points are
compared

36. Summary
 To calculate t-test, we need two t-values:
– Calculated t-value
– Critical t-value
 If calculated t-value is greater than critical t-
value, then reject the null hypothesis.
 In SPSS:
– analyze for normal distribution
– Perform the test
– If the sig < alpha value, null hypothesis will be
accepted

37. Reference
 Stacey B., Laurel S. (1st
edtion). Statistics for
Nursing and Allied Health