An Introduction to Hypothesis Testing

2.  It is a method that makes use of sample data
to make evaluations regarding a population

3.  Identify the populations, comparison
distribution, and the assumptions
◦ Assumptions: characteristics that we ideally require
the population from which we are sampling to have
so that we can make accurate inferences
 Interval/Ratio Level
 Normality
 Independence
 Homogeneity of Variance
 State the null and research hypothesis
 Null Hypothesis: “There is no relationship/difference
between ________ and __________”
 Research Hypothesis: “There is a
relationship/difference between ________ and

4.  Determine characteristics of comparison
distribution
◦ Describes the distribution represented by the null
hypothesis
◦ These values will be used in the actual calculations
 Determine critical values/cutoff
◦ Critical Values: test statistic values beyond which
we reject the null hypothesis
◦ Critical Region: area in the tails of comparison
distribution which we reject the null hypothesis if
our test statistic falls there.
◦ Alpha level (p level): probabilities determining the
critical values

5.  Calculate the test statistic
 Make a conclusion
◦ Depends on the kind of test
 One-Tailed
 Left Tailed:
 H0: μ1 ≥ μ2
 H1: μ1 < μ2
 Right Tailed
 H0: μ1 ≤ μ2
 H1: μ1 > μ2
 Two-Tailed
 H0: μ1 = μ2
 H1: μ1 ≠ μ2

6.  Level of Significance: The probability or
rejecting the null hypothesis when it is true.
The probability of Type I Error
 Type I Error: rejecting a true null hypothesis
◦ Concluding that there is an effect, when there is not
◦ 1-α
 Type II Error: failure to reject a false null
hypothesis
◦ 1-β
◦ Concluding that there is no effect, when there is

7.  It is the interval estimate of the sample
statistic which includes the population mean
if we sampled from the same population
◦ Point Estimate: summary statistic from a sample
that is just one number used s an estimate of the
population parameter
◦ Interval Estimate: provides a range of plausible
values for population parameter

8.  Indicates how much difference there is
between a sample and a population
 Describes the absolute magnitude of a
treatment effect
𝐶𝑜ℎ𝑒𝑛′
𝑠 𝑑 =
𝑀 − 𝜇
𝜎
 0.20 = “small”
 0.50 = “medium”
 0.80 = “large’

9.  Measure of the ability to reject the null
hypothesis given that it is false.
 Probability of not making a Type II Error