This presentation describes the concept of One Sample t-test, Independent Sample t-test and Paired Sample t-test. This presentation also deals about the procedure to do the t-test through SPSS.

1. One Sample t-test
Independent Sample t-test
&
Paired Sample t-test
K.THIYAGU,
Assistant Professor, Department of Education,
Central University of Kerala, Kasaragod

2. Statistical Analysis
Control
Group
Mean
Treatment
Group
Mean
Is there a difference?

3. Low
variability
What Does Difference Mean?
High
variability
Medium
variability

4. Low
variability
What Does Difference Mean?
High
variability
Medium
variability
The mean difference
is the same for all
three cases.

5. Low
variability
What Does Difference Mean?
High
variability
Medium
variability
The mean difference
is the same for all
three cases.
Which one shows
the greatest
difference?

6. What Do We Estimate?
Low
variability
Signal
Noise

7. What Do We Estimate?
Low
variability
Signal
Noise
Difference between group means
= =t

8. What Do We Estimate?
Low
variability
Signal
Noise
Difference between group means
Variability of groups
= =t

9. What Do We Estimate?
Low
variability
Signal
Noise
Difference between group means
Variability of groups
=
=
XT - XC
SE(XT - XC)
_ _
_ _

10. Independent
Samples
Related
Samples
Interval
measures /
parametric
Independent
samples t-test*
Paired samples
t-test**
Ordinal/
Non-parametric
Mann-Whitney
U-Test
Wilcoxon test
* 2 experimental conditions and different participants were assigned to each condition
** 2 experimental conditions and the same participants took part in both conditions of the experiments

11. DSE
MM
t 21 −
=
‘t’- Test It was introduced by William Sealy Cosset
Compare the mean between 2 samples/ conditions

12. One Sample t-test

13. The One Sample t -Test is a parametric test.
whether the
sample mean
is statistically
different
from a known
or
hypothesized
population
mean
determines
One
Sample
t -Test

14. One Sample
t-test Single
Sample t -Test
Sample
Mean
Population
Mean
Determine
the
Statistically
Different
of

15. The dependent variable must be continuous (interval/ratio).
The observations are independent of one another.
The dependent variable should not contain any outliers.
The dependent variable should be approximately normally
distributed.
Assumptions – One Sample t-test

16. Hypotheses
where µ is a constant proposed for the
population mean and x is the sample mean.
Null
Hypothesis (H0)
H0: µ = x
"The sample mean is
equal to the [proposed]
population mean"
Alternative
Hypothesis (H1)
H1: µ ≠ x
"The sample mean is not
equal to the [proposed]
population mean"

17. Analyze
Compare
Means
One-Sample
T Test.
Run a One Sample t-Test (SPSS)

18. •Test value in the One-Sample T Test window.A) Test Value
•The test statistic of the one-sample t test, denoted t. Note that t is calculated by
dividing the mean difference (E) by the standard error mean (from the One-Sample
Statistics box).
B) t Statistic
•The degrees of freedom for the test. For a one-sample t test, df = n - 1;C) df
•The two-tailed p-value corresponding to the test statistic.D) Sig. (2-tailed)
•The difference between the "observed" sample mean (from the One Sample
Statistics box) and the "expected" mean (the specified test value (A)).
E) Mean Difference:
•The confidence interval for the difference between the specified test value and the
sample mean.
F) Confidence
Interval for the
Difference:

19. Independent
Sample
t-test

20. The Independent Sample t -Test
is a parametric test.
whether there is
a statistically
significant
difference
between the
means in
two unrelated
groups.
determines
Independent
Sample
t -Test

21. Independent t -Test is also known as
Independent Measures t Test
Independent Two-sample t Test
Student t Test
Two-Sample t Test
Uncorrelated Scores t Test
Unpaired t Test
Unrelated t-test

22. The dependent variable must be continuous (interval/ratio).
The independent variable should consist of two categorical independent
groups.
Independence of observation
No significant outliers
The dependent variable should be approximately normally distributed.
Assumptions – Independent Sample t-test

23. Hypotheses of Independent Sample t-test
Where µ1 and µ2 are the population means for
group 1 and group 2, respectively.
Null
Hypothesis (H0)
H0: µ1 = µ2
H0: µ1 - µ2 = 0
"The two population
means are equal"
Alternative
Hypothesis (H1)
HA: µ1 ≠ µ2
H1: µ1 - µ2 ≠ 0
"The two population
means are not
equal"

24. Hypotheses of Levene’s Test for Equality of Variances
Where σ1
2 and σ2
2 are the population variances for
group 1 and group 2, respectively.
Null
Hypothesis (H0)
H0: σ1
2 - σ2
2 = 0
"The population
variances of group 1
and 2 are equal"
Alternative
Hypothesis (H1)
H1: σ1
2 - σ2
2 ≠ 0
"The population
variances of group 1
and 2 are not equal"

25. Analyze
Compare
Means
Independent
Sample T Test.
Run a Independent Sample t-Test (SPSS)
SPSS

26. Independent Sample ‘t’ test
Analyze
Compare Means
Independent sample ‘t’ test
Independent test
▪IV : No. of groups (categorical-two groups)
▪DV : Scores in Problem Solving (interval)
Ho: There is no significant difference between control and experiment group students in their post test score.

27. • F is the test statistic of Levene's test. Sig. is the p-value corresponding to this test
statistic.
A) Levene's Test for
Equality of Variances
•The test statistic of the one-sample t test, denoted t. Note that t is calculated by
dividing the mean difference (E) by the standard error mean (from the One-Sample
Statistics box).
•The degrees of freedom for the test. For a one-sample t test, df = n - 1;
B) t Statistic & df
•The two-tailed p-value corresponding to the test statistic.Sig. (2-tailed)
•Mean Difference is the difference between the sample means; it also corresponds to
the numerator of the test statistic
Mean Difference
•It is the standard error; it also corresponds to the denominator of the test statisticStd. Error Difference
•The confidence interval for the difference between the specified test value and the
sample mean.
C) Confidence Interval
for the Difference

28. Paired Sample t-test

29. The Paired Sample t -Test is a parametric test.
whether there is
statistical evidence
that the mean
difference between
paired observations
on a particular
outcome is
significantly different
from zero
determines
Paired
Sample
t -Test
The Paired Samples t Test compares two means that are from the same
individual, object, or related units.

30. Paired Sample t -Test is also known as
Dependent t Test
Dependent Sample t Test
Repeated Measures t Test
Correlated Scores t Test
Paired t Test

31. The dependent variable must be continuous (interval/ratio).
The independent variable should consist of two categorical
‘related groups’ or ‘matched pairs’.
No significant outliers
The dependent variable should be approximately normally
distributed.
Assumptions – Paired Sample t-test

32. Hypotheses of Paired Sample t-test
Where µ1 is the population mean of variable 1, and
µ2 is the population mean of variable 2.
Null
Hypothesis (H0)
H0: µ1 = µ2
H0: µ1 - µ2 = 0
"The paired
population means
are equal"
Alternative
Hypothesis (H1)
HA: µ1 ≠ µ2
H1: µ1 - µ2 ≠ 0
"The paired
population means
are not equal"

33. Analyze
Compare
Means
Paired
Sample T Test.
Run a Paired Sample t-Test (SPSS)

34. Paired Sample ‘t’ test
Analyze
Compare Means
Paired sample ‘t’ test
Ho: There is no significant difference between pre test and post test means scores of experiment group students
Paired test
Two test (same sample – different interval test): Interval Scales

35. Thank You