Testing Statistical Hypothesis The One Sample t-Test. Heibatollah Baghi, and Mastee Badii. Parametric and Nonparametric Tests. Parametric tests estimate at least one parameter (in t-test it is population mean)
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Testing Statistical HypothesisThe One Sample t-Test
Heibatollah Baghi, and
Mastee Badii
Usually for normal distributions and when the dependent variable is interval/ratio
Distribution-free tests
Although appropriate for all levels of measurement most frequently applied for nominal or ordinal measures
What is type two error?
This lecture focuses on
One sample t-test
which is a parametric test
True
False
True
(Accept Ho)
Type II error
Probability = b
False
(Rejects Ho)
Type I error
Probability = a
True
False
True
(Accept Ho)
Correct decision
Probability = 1- a
Type II error
Probability = b
False
(Rejects Ho)
Type I error
Probability = a
Correct decision
Probability = 1- b
True
False
True
(Accept Ho)
Correct decision
Probability = 1- a
Type II error
Probability = b
False
(Rejects Ho)
Type I error
Probability = a
Correct decision
Probability = 1- b
Population of IQ scores, 10-year olds
µ=100
σ=16
n = 64
Sample 1
Sample 2
Sample 3
Etc
This lecture focuses on
one sample t-test
The One Sample t – Test
Testing statistical hypothesis about µ when σ is not known OR sample size is small
Population mean
Small sample
Population variance is unknown & estimated from sample
A two tailed
test because it
can be either larger
or smaller
Sample mean
Deviation
from sample
mean
Squared
deviation
from
sample
mean
Standard deviation of observations
Calculated
t value
Standard deviation
of sample means
Calculated t
X
--------
--------
--------
Decision Rule for t-Scores
If |tc| > |tα| Reject H0
Decision Rule for P-values
If p value < α Reject H0
Pvalue is one minus
probability of observing
the t-value calculated
from our sample
|tc = 2.449| > |tα= 2.262| Reject H0
If p value = .037 < α = .05 Reject H0
Standard deviation of sample means
Sample mean
Critical t value
In drawing samples at random, the probability is .95 that an interval constructed with the rule
will include m
One Sample t-test Testing Neutrality of Attitudes Towards Infertility Alternatives
N
Mean
Std. Deviation
Std. Error Mean
Number of Hours
10
9.90
4.067
1.286
Test Value = 6.75
tc
df
Sig. (2-tailed)
Mean Difference
95% Confidence Interval of the Difference
Lower
Upper
Number of Hours
2.449
9
.037
3.150
.24
6.06
SPSS Output: One-Sample Statistics
One-Sample Test
Take Home Lesson
Procedures for Conducting & Interpreting One Sample Mean Test with Unknown Variance