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Hypothesis Testing (Chapter 8)
 Definition: Hypothesis testing is an inferential procedure where
sample data is used to evaluate the credibility of a hypothesis
about a population
 Important assumption: That the effect of a treatment is to add
or subtract a constant from each individual’s score. This
implies that after the treatment, the population has:
 The same shape
 The same standard deviation
 Sometimes the effect of a treatment is obvious and sometimes it
is not (example)
 Because of the possibility of researchers making errors when
judging experimental effects, a standardized procedure for
hypothesis testing has been developed
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Hypothesis testing procedure: General overview
1)
The researcher states 2 opposing hypotheses:
 The null hypothesis or Ho
 The scientific, working or alternate hypothesis H1
For example: A researcher is examining the effects of increased
handling (stimulation) on the physical development of children
 The national data shows a population mean of 26 lbs. for 2 year
olds
 The researcher must compare the sample data (children who
have experienced increased handling) with the population mean
Hypotheses:
 Ho states that the treatment has no effect – additional handling
has no effect on body weight of the population of 2 year olds
Ho: u infants handled = 26 lbs.
 In an experimental context, Ho predicts that IV (independent
variable or treatment variable) has no effect on the dependent
variable (DV) for the population – in this case weight
 H1 states the opposite of Ho – that the treatment (IV) does
produce a change in the DV for the population
H1: u infants handled does not equal 26 lbs.
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 Note: H1 does not specify the direction of change created by the
treatment – directional hypotheses tests will be discussed later
 When not specifically asked to carry out a directional
hypothesis test, always carry out a non-directional test
 generally non-directional tests are the most conservative and,
therefore, the most appropriate
2)
The question the researcher has to answer is whether
differences between the sample statistics and the population
parameters are the result of the treatment or the result of
sampling error – standardized criteria are set to answer this
question in an objective manner
Example:
3)
Collect sample data:
 Sample of infants obtained objectively
 Parents trained to provide additional handling
 Infants’ body weights measured when children reach
2 yrs
4)
Evaluate Ho:
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 Data from the sample, after treatment, are compared with Ho –
there are 2 possible outcomes:
 Reject Ho – the treatment has an effect
 Fail to reject Ho – treatment has no effect
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Types of errors that can be made in hypothesis testing:
Type 1 errors: reject Ho when the treatment in fact has no effect
(falsely finding)
Type 2 errors: fail to reject Ho when in fact the treatment has an
effect, in other words, failing to reject a null hypothesis that is
really false (fail to find)
Table:
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 We can’t be certain if our decision to reject or fail to reject Ho
is correct but we can figure out the probability of being right or
wrong
 The hypothesis testing procedure is structured so that the
researcher can specify and control the probability of making a
Type 1 error (falsely finding an effect) – this probability is
always kept very low
 We need to determine which sample means are likely if Ho is
true and which are unlikely – the term significance refers to the
probability value which is used to define ‘unlikely’ and is
generally set at 0.05 (5%) – we also call this the alpha level

 For example:
 0.05 (5% probability that the effect occurred by
chance - most common value used criterion for
publication – set by Ronald Fisher 1925)
 0.01 (1% probability that the effect occurred by
chance - criterion for publishing in some prestigious
scientific journals
 0.001 (0.1% probability that the effect occurred by
chance - criterion for publishing in some prestigious
scientific journals
 0.1 trend
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 The alpha level is used to divide the distribution of sample
means into 2 parts:
 Sample means comparable with Ho
 Sample means significantly different from Ho
 We reject Ho if the sample mean after the treatment
is in the extreme tails of the distribution of sample
means. Therefore, the alpha level defines the
probability of making a Type 1 error (max 5%)
Steps to evaluating hypothesis:
1)
2)
3)
4)
State the hypotheses (Ho and H1) and define the alpha level
Use the alpha level to define data that would reject Ho
Analyze sample data
Make a decision about Ho
Note: For non-directional tests, alpha is divided evenly between
the 2 tails of the distribution of sample means – these areas in the
tails are called critical regions or regions of rejection (rejection of
Ho)
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Test statistic: various test statistics can be used to evaluate a
hypothesis from sample data one which we can use is the Z
Z
x
x
obtained difference/difference due to chance
Failure to reject Ho:
 We don’t prove that Ho is true because a sample provides
limited information about a population
 Researchers, therefore don’t say that they ‘accept’ Ho but
instead that they ‘fail to reject’ Ho
 By having a low alpha (0.05) we are actually increasing the
chance of a Type 2 error (failing to find an effect when one is
really there) but this is generally viewed as a less serious error
than a Type 1 (falsely finding an effect when one isn’t really
there)
 Alpha defines the risk of a Type 1 error but there is no method
of specifying the chance of a Type 2 error (beta)
 For alpha:
 0.05
 0.01
 0.001
Z= +/- 1.96
Z= +/- 2.58
Z= +/- 3.30
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In the literature:
 Example: The results indicate that increased handling has a
significant effect on the weight of 2 year olds, Z = __ p<0.05
Assumptions for hypothesis testing:
 Sample data is obtained randomly
 Observations are independent (orthogonal) no consistent
relationship between observations – usually met by random
sampling
 Assume standard deviation remains unchanged by treatment
 Distribution of sample means must be normal (stated in question
or n at least 30)
Directional tests (one tailed):
 Use of directional tests is warranted but not recommended
Example of distribution:
 Slightly different phrasing of Ho and H1,
Note: usually easier to start with H1
H1: u with infant handling > 26 lbs.
Ho: u without infant handling ≤ 26 lbs.
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 Some say 1 tailed test makes it too easy to refute Ho and,
therefore, too easy to make a Type 1 error
 Some like to use 1 tailed test for exploratory research (pilot
studies) – generating of new research possibilities
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