KNR 445

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Stage 5 The test statistic!
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• So, we insert that threshold value, and now we
  are asked for some more values

The sample mean
The sample size
The population SD
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Stage 5 The test statistic!

• Why do we need these three? Because now we have
  to convert our difference score to a score on the
  distribution of sample means
• Remember this?

The purpose of this statistic was to convert a
raw score difference (from the mean) by scaling
it according to the spread of raw scores in the
distribution of raw scores
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Stage 5 The test statistic!
The purpose of this statistic is the same, but it
converts a sample mean difference (from µ) by
scaling it according to the spread of all sample
means in the distribution of sample means
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Stage 5 The test statistic!

• Understanding influences on the distribution of
  sample meanswell use the applet again

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Note sample size
note spread of sample means
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Stage 5 The test statistic!

• Understanding influences on the distribution of
  sample meanswell use the applet again

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As sample size goes up
Spread of sample means goes down
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Stage 5 The test statistic!

• Understanding influences on the distribution of
  sample means
• That means that the test statistic has to take
  sample size into account
• Other influences are mean difference (sample
  population) and variability in the population
• How do you think each of these things influence
  the test statistic?
• This will help you understand why the test
  statistic looks like it does

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Stage 5 The test statistic!
A closer look to understand how the mean
difference, population variance, and sample size
affect the test statistic, we need to look at the
SEM in more detail
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Stage 5 The test statistic!
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Population standard deviation
Socan you see the influences?
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Sample size
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Stage 5 The test statistic!

• To calculate, then
• First the standard error of the mean
• Now the test statistic itself

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Stage 5 The test statistic!

• For you to practice, Ive provided a simple excel
  file that does the calculation bit for you

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Stage 6 The comparison decision

• Do we fail to reject the null? Or reject the null?

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3 ways of phrasing the decision

• What is the probability of obtaining a Zobs
  1.273 if the difference is attributable only to
  random sampling error?
• Is the observed probability (p) less than or
  equal to the ?-level set?
• Is p ? ? ?

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Reporting the Results

• The observed mean of our treatment group was
  51.88 (? 13.62) pages per employee per week. The
  z-test for one sample indicates that the
  difference between the observed mean of 51.88 and
  the population average of 49.52 was not
  statistically significant (Zobs 1.27, p gt 0.1).
  Our sample of employees did not use significantly
  more paper than the norm.

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Do not reject H0 vs. Accept H0

• Accept infers that we are sure Ho is valid
• Do not reject implies that this time we are
  unable to say with a high enough degree of
  confidence that the difference observed is
  attributable to anything other than sampling
  error.

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