Hypothesis Testing

1
Hypothesis Testing

• A hypothesis is an assumption that appears to
  explain certain phenomena, which must be tested
  to see whether or not it is true

2
Usually thought of as the total number of
inhabitants of a given area, but in research, a
population refers to the units from which a
sample is drawn.
Population
Random Selection
A subset of a population that is selected for a
given study.
Sample
Random Assignment
Group A
Group B
Drugs
Chiropractic
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Drug Drug Drug Drug Chiropractic Chiropractic
Case ROM ROM ROM Case ROM
A1 30 B1 50
A2 50 B2 70
A3 60 B3 80
A4 40 B4 60
A5 70 B5 90
A6 50 B6 70
A7 30 B7 50
A8 60 B8 80
A9 50 B9 70
A10 70 B10 90
A11 60 B11 80
A12 50 B12 70
A13 30 B13 50
A14 40 B14 60
Group A
Group B
Low-back pain patients
4
The Hypothesis (H1)

• Chiropractic patients will have better ROM than
  Drug patients
• To see if this is true, compare the average ROM
  of the Drug group with the average ROM of the
  Chiropractic group
• Drug50 degrees
• Chiropractic70 degrees
• Is this difference real or merely due to chance?

5
Coin Toss Probability

• Hypothesis testing deals with probabilities
• In a coin toss, what is the probability of
  getting heads or tails?
• The probability of getting heads the
  probability of getting tails (0.5 or 50)

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Coin Toss Cont.

• How about getting 2 heads in 2 tosses? (½ X ½
  ¼) 0.25
• 50 tosses
• Likely to get around 25 H and 25 T
• Unlikely to get 10 H and 40 T
• Highly unlikely (but not impossible) to get 49 H
  and 1T

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Research (Alternative) Hypothesis (H1) vs. Null
Hypothesis (H0)

• The null hypothesis assumes that there is no
  difference between the groups being tested
• The research hypothesis is to be adopted only if
  the null hypothesis proves unlikely
• In biomedical research it typically must be at
  least 95 unlikely
• Similar to the innocent until proven guilty
  concept in our legal system

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Mean (average)
A1 30
A2 50
A3 60
A4 40
Variability(Spread)
A5 70
A6 50
A7 30
A8 60
A9 50
A10 70
A11 60
A12 50
A13 30
A14 40
10 20 30 40 50 60 70 80
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A1 30 (-20)
A2 50
A3 60 (10)
Deviations from the mean
A4 40 (-10)
A5 70 (20)
A6 50
A7 30 (-20)
A8 60 (10)
A9 50
A10 70 (20)
A11 60 (10)
A12 50
A13 30 (-20)
A14 40 (-10)
10 20 30 40 50 60 70 80
10
-2010-1020-20102010-20-10 0
400100100400 400 100 400 100400
100 2500/13 192.3
Add squared deviations, then divide by n-1 to get
the Variance
The square root of the Variance is the Standard
Deviation
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Drug
50 70
Chiro
Hypothesis testing involves comparing means,
which seems obvious at first


50 70


Chiropractic appears to clearly be superior
50 70


50 70


20 30 40 50 60 70 80 90 100
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• Consider a study dealing with chiropractic
  adjustments for tension headaches
• There was 38 improvement with chiropractic
• 23 with placebo
• 29 with a drug

The question is . . . are these differences
enough to say that chiropractic was better?
How much difference is needed to be significant?
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Statistical Significance

• The term indicating that a studys results are
  unlikely to be the result of chance at a
  specified probability level, leading to rejection
  of the H0 and acceptance of the H1

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Statistical Significance

• Something is statistically significant if it is
  unlikely that the event would occur by chance
  less than a specific proportion of the time
• If no specific proportion is given, the 5 level
  is assumed

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Statistical Significance

• In statistics significant means probably true
  (not due to chance)
• A research finding may be true without being
  important (not clinically significant)
• When researchers say a result is highly
  significant they mean it is very probably true
• They do not (necessarily) mean it is highly
  important

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30 50
SD 13.9
50 70
60 80
40 60
70 90
50 70
30 50
60 80
50 70
70 90
60 80
50 70
t-test Significance 0.001
30 50
40 60
20 30 40 50 60 70 80 90 100
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Significance of 0.001

• Significance of 0.001 means that the likelihood
  that the conclusion was a mistake is only 0.1
• You can be 99.9 confident that the decision to
  accept the H1 was a correct decision . . . that
  chiropractic care appears to be better than drugs
  for low-back pain

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30 40
SD 13.9
50 60
60 70
40 50
70 80
50 60
30 40
60 70
50 60
70 80
60 70
Significance 0.067 (not significant ), so the
means cannot be considered to be different
50 60
30 40
40 50
20 30 40 50 60 70 80 90 100
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P-value

• P 0.05 is the typical cutoff point in
  biomedical research (AKA a)
• Which means you can be 95 confident that the
  decision was correct
• P-values above 0.05 are not significant and the
  studys hypothesis would not be supported

Your decision to conclude that the means were
different and Chiropractic was better than Drugs
20
30 50
A SD 13.9
50 60
B SD 6.2
6060
40 60
7070
50 60
30 50
6060
50 60
7070
6060
50 60
t-test Significance 0.032
30 50
40 60
20 30 40 50 60 70 80 90 100
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How the results of this study would appear in a
journal

• Chiropractic was found to be superior to drug
  therapy in improving lumbar ROM in a group of
  low-back pain patients (Plt0.05)
• The Balon et al. asthma study . . . No
  significant differences between the groups in the
  degree of change from base line (morning peak
  expiratory flow, P0.49 at two months and P0.82
  at four months).

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• Histogram of Group A
• Adjoining bars represent
• the frequency of each value

Notice the values form a shape
5 4 3 2 1
50
30 50 60
30 40 50 60 70
30 40 50 60 70
30 40 50 60 70 80 90 100
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Normal curve
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Relationship between 95 CIs and P values

• Information about the P value is contained in the
  95 CI
• The P value can be inferred based on whether the
  finding of no difference falls within the CI

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Caution

• A 95 chance of something being true means there
  is a 5 chance of it being false
• This means that of every 100 tests that show
  results significant at the 95 level, the odds
  are that five of them are false
• If you took a totally random set of data and did
  100 significance tests, about five tests would be
  falsely reported to be significant

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Summary

• Hypothesis testing determines whether or not a
  studys results are significant.
• The means of the different groups are commonly
  compared using a t-test.
• P-value must be equal to or less than 0.05
  (typically).
• There is a 5 or less chance that the conclusion
  is wrong.

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Decision to accept or reject depends upon
The amount of the difference between the means
50
Variability of the data (standard deviation)
A large difference between means and a low
standard deviation is best