One-Sample t-Test
What It Is: A one-sample t-test is used to determine whether the mean of a single
sample is significantly different from a known or hypothesized population mean.
When to Use It: Use this test when you have a single sample and you want to
compare its mean to a specific value (e.g., a population mean).
Example: Testing if the average height of a sample of students is different from the
national average height.
Assumptions:
> Variable should come from a normal distribution or n>30
> Variable is Interval or Ratio level
> Sample is randomly selected and independent
How to Use It:
1. Formulate Hypotheses:
○ Null hypothesis H0: There is no difference between sample and the
population
○ Alternative hypothesis H1: There is a difference between the sample
and the population.
2. Run SPSS:
Analyze → Compare Means → One- Sample T-test
Test Value → Hypothetical Population mean
3. Interpret the Results:
○ t-Value: Indicates how many standard errors the sample mean is from the
population mean.
○ p-Value: If p < 0.05, reject the null hypothesis.
○ Confidence Interval: Range within which the true population means lies with a
certain level of confidence (usually 95%).
For one sample t-test we add the test value to the intervals to receive the
intervals for sample not for population.
Interval does not include the value of the null hypothesis (population mean) →
The test is significant which means that the sample comes from a different
population WE REJECT THE NULL HYPOTHESIS.
,Reporting: test value, mean, standard deviation, t-score & df {t(df)=score for t},
p-value, Cohen’s d, 95% CI and do we reject or retain the null hypothesis.
Cohen’s D
0.20 small effect size
0.50 moderate effect size
0.80 large effect size
Reporting APA 7:
The one-sample t-test showed that in the sample of students the average exam
grade is significantly higher than 6.146, the exam grade in the population of
students: (M=6.63, SD= 1.75), t(236)=4.28. p<0.001, d=0.28, 95% CI [6.4, 6.86].
We reject the null hypothesis.
, Paired Sample t-Test
What It Is: A paired sample t-test compares the means of two related groups to
determine if there is a significant difference between them.
When to Use It: Use this test when you have two measurements from the same
group (e.g., before and after a treatment).
Example: Comparing the average test scores of students from two different
schools.
Assumptions:
> Variable should come from a normal distribution or n>30
> Variable is Interval or Ratio level
> Sample is randomly selected and independent
How to Use It:
1. Formulate Hypotheses:
○ Null hypothesis H0: In the population, the mean score on day 1 is not
different from the mean score on day 3.
○ Alternative hypothesis H1: In the population, the mean score on day 1
is different from the mean score on day 3.
2. Run SPSS:
Analyze → Compare Means → Paired sample t-test
Variable 1: post ; Variable 2: pre (anti chronological order)
3. Interpret the Results:
○ t-Value: Indicates the size of the difference relative to the variation in
your sample data.
○ p-Value: If p < 0.05, reject the null hypothesis.
○ Confidence Interval: Indicates the range of values within which the
true mean difference lies.
Interval does not include the value of the null hypothesis (population
mean) → The test is significant which means that the sample comes
from a different population WE REJECT THE NULL HYPOTHESIS.
What It Is: A one-sample t-test is used to determine whether the mean of a single
sample is significantly different from a known or hypothesized population mean.
When to Use It: Use this test when you have a single sample and you want to
compare its mean to a specific value (e.g., a population mean).
Example: Testing if the average height of a sample of students is different from the
national average height.
Assumptions:
> Variable should come from a normal distribution or n>30
> Variable is Interval or Ratio level
> Sample is randomly selected and independent
How to Use It:
1. Formulate Hypotheses:
○ Null hypothesis H0: There is no difference between sample and the
population
○ Alternative hypothesis H1: There is a difference between the sample
and the population.
2. Run SPSS:
Analyze → Compare Means → One- Sample T-test
Test Value → Hypothetical Population mean
3. Interpret the Results:
○ t-Value: Indicates how many standard errors the sample mean is from the
population mean.
○ p-Value: If p < 0.05, reject the null hypothesis.
○ Confidence Interval: Range within which the true population means lies with a
certain level of confidence (usually 95%).
For one sample t-test we add the test value to the intervals to receive the
intervals for sample not for population.
Interval does not include the value of the null hypothesis (population mean) →
The test is significant which means that the sample comes from a different
population WE REJECT THE NULL HYPOTHESIS.
,Reporting: test value, mean, standard deviation, t-score & df {t(df)=score for t},
p-value, Cohen’s d, 95% CI and do we reject or retain the null hypothesis.
Cohen’s D
0.20 small effect size
0.50 moderate effect size
0.80 large effect size
Reporting APA 7:
The one-sample t-test showed that in the sample of students the average exam
grade is significantly higher than 6.146, the exam grade in the population of
students: (M=6.63, SD= 1.75), t(236)=4.28. p<0.001, d=0.28, 95% CI [6.4, 6.86].
We reject the null hypothesis.
, Paired Sample t-Test
What It Is: A paired sample t-test compares the means of two related groups to
determine if there is a significant difference between them.
When to Use It: Use this test when you have two measurements from the same
group (e.g., before and after a treatment).
Example: Comparing the average test scores of students from two different
schools.
Assumptions:
> Variable should come from a normal distribution or n>30
> Variable is Interval or Ratio level
> Sample is randomly selected and independent
How to Use It:
1. Formulate Hypotheses:
○ Null hypothesis H0: In the population, the mean score on day 1 is not
different from the mean score on day 3.
○ Alternative hypothesis H1: In the population, the mean score on day 1
is different from the mean score on day 3.
2. Run SPSS:
Analyze → Compare Means → Paired sample t-test
Variable 1: post ; Variable 2: pre (anti chronological order)
3. Interpret the Results:
○ t-Value: Indicates the size of the difference relative to the variation in
your sample data.
○ p-Value: If p < 0.05, reject the null hypothesis.
○ Confidence Interval: Indicates the range of values within which the
true mean difference lies.
Interval does not include the value of the null hypothesis (population
mean) → The test is significant which means that the sample comes
from a different population WE REJECT THE NULL HYPOTHESIS.
