Stats 1 data presentation

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• Lecture 7
• Two sample t-test
• Part 2 - Interpreting a t-value
• - p-values
• - Significance
• - Using Minitab to perform a
  t-test
• - Error types
• - Power

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Judging the t-value
Question If the null hypothesis were true, how
often would get a t-value as high as this
one? This is the infamous p-value.
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High p value
e.g. p 0.4 If there was no real treatment
effect, we would still get t values this great
40 of the time, by simple chance. Data is not
adequate to justify any positive claims.
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Low p value
e.g. p 0.0001 If there was no real treatment
effect, we would get t values this great only
0.01 of the time. Data is adequate to justify a
positive claim.
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p lt 0.05
By convention, we declare the evidence adequate
when p lt 0.05. If you are faced with a situation
where there is no real effect, there is only a 5
chance that you will suffer
Large difference between sample means
False positive finding
Freak samples
Large t-value
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p lt 0.05
Defines our standard of proof. When faced with
situations where there is no real treatment
effect, you will arrive at a correct conclusion
95 of the time.
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Jargon (1)
The remaining 5 of cases where we (falsely)
declare that we have found an effect, is
a False positive or Type I error
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Jargon (2)
When we decide that the there is a real effect
we Reject the null hypothesis The results
are then called Significant Note The
opposite is Non-significant not Insignificant
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Jargon (3)
The limiting p-value below which we declare our
results to be significant (usually 0.05) is known
as the ? value
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Using Minitab to perform the two sample t-test on
the Aldostero data
Follow the menus Stat Basic Statistics 2-Sample
t...
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1) Click button for data in 2 columns
Setting up the t-test
2) Enter names of the 2 columns.
3) OK
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Output from the t-test
t-value (Ignore the minus)
p-value
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Aldostero
As the calculated p-value is less than 0.05 we
would conclude that The experimental data
provides significant evidence that the use of
Aldostero does alter the handling of sodium (p
0.025).
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Correct understanding of significant.

• If Aldostero actually had no effect upon sodium
  handling, then there is less than a 5 chance
  that we would obtain random samples which
  provided this much apparent evidence of an
  effect.
• We are not saying that we have absolute proof of
  an effect.
• We are saying that the evidence is of value and
  deserves to be considered along with any other
  relevant information that may be available.

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Power
If there really is a treatment effect of a
certain size, what are the chances that we will
detect it and declare it to be statistically
significant?
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Power
Almost certain to demonstrate significance
Sample size
Almost no chance of demonstrating significance
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Jargon (4)
Failing to detect an effect that is in fact
present is called a False negative or Type
II error
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Jargon (5)
The chances of failing to detect an effect that
really is present is called the ? value
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Power
Since ? is the likelihood of failing to detect an
effect that is present
Power 1 - ?
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Is there really an effect?
Yes
No
Do we detect an effect?
True positive
False positive Type I error
Yes
False negative Type II error
True negative
No
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Jargon summary
Type I error False positive ?
Type II error False negative b
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Terms with which you should be familiar

• p-value
• Significance
• Type I error
• Type II error
• ?
• ?
• Power

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What you should be able to do

• Describe the information conveyed by a p-value.
• Use Minitab to perform a two sample t-test.
• Distinguish between a Type I and a Type II error.
• Describe the information conveyed when a result
  is described as Significant.
• Describe the information conveyed by the Power
  of an experiment.
• Describe the relationship between power and
  sample size