Chapter 10 - Hypothesis Testing + Sign Test

James A. Van Slyke
Azusa Pacific University
Purpose –
◦ Allows a scientist to test the influence of the
independent variable upon the dependent variable
◦ Controls for the influence of other variables
◦ Primary question – “How reasonable are these
results if chance alone were responsible?”
◦ If the results are not due to chance, then the results
are attributed to the experimental manipulation
Repeated Measures Design
◦ One of several commonly used designs
◦ Replicated Measures Design or Correlated Groups
 Subjects are paired prior to conducting experiment
 Difference between paired scores is analyzed
Two Experimental Groups
◦ Experimental – Receives treatment
◦ Control Group – No Treatment (placebo)
Alternative Hypothesis (H1)
◦ Claims that difference in results between the two
conditions is due to the independent variable
Directional Hypothesis
◦ Specifies the direction of the effect of the
independent variable
Nondirectional Hypothesis
◦ The independent variable has an effect but the
direction is not specified
Logical counterpart of alternative hypothesis
◦ Nondirectional – the independent variable has no
effect on the dependent variable
◦ Directional – the independent variable has no effect
in that specific direction on the dependent variable
The alternative hypothesis and the null
hypothesis are mutually exclusive and
If one is true the other must be false and vice
The experiment attempts to show that the null
hypothesis is false
Obviously if the null hypothesis is false, the
alternative hypothesis can be accepted as true
The null hypothesis is evaluated directly
because it is possible to calculate the
probability of chance events
But, there are no mathematics for the
alternative hypothesis
The focus in on the null hypothesis to
support accepting the alternative hypothesis
Chance – the probability of the results is
compared to that of chance
Alpha level – If the probability is less then or
equal to the value of alpha, the null
hypothesis is rejected
When the null hypothesis is rejected, the
results are thought to be significant or
Level of alpha is dependent upon the
particular experiment
A lpha level = 
C om m on levels for alpha
  0.05
  0.01
Type I – Null hypothesis is rejected when it is
actually true
◦ Probability of Type I error set by alpha
Type II – Null hypothesis is retained when it is
actually false
◦ Probability of making a Type II error is called beta
Increasing alpha decreases beta and vice versa
Setting alpha and beta depends upon the cost
of making either type of error
Directional Hypothesis – determine the
probability of getting an outcome or an even
more extreme score
◦ Evaluate the tail of the distribution
Nondirectional hypothesis – probability of
obtaining an extreme score in both direction
◦ Evaluate both tails of the distribution
Two-tailed probability – without valid basis
for directional hypothesis, indirectional used
One-tailed probability – Used for directional
◦ If there is a good theoretical basis
◦ If there is other data supporting the conclusion
Used only in replicated measures
◦ 1. Null and alternative hypothesis generated
◦ 2. Directional or nondirectional
◦ 3. Alpha level set
Difference between control group and
experimental calculated
Sign of the difference recorded
Magnitude of difference ignored
Ties are ignored
Assumptions of binomial distribution must be
◦ Probability of getting results and more extreme
◦ Use one or two-tailed binomial distribution
depending on hypothesis
◦ Compare probability to alpha
Draw appropriate conclusions and
Results that are statistically significant are
Yet statistically significant does not mean a
large effect
Effects are dependent upon their particular
size and their reliability
4, 5, 7, 9, 10
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