Statistical Fridays

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Statistical Fridays

• J C Horrow, MD, MSSTAT
• Clinical Professor, Anesthesiology
• Drexel University College of Medicine

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Previous Session Review

• Tests involve a NULL hypothesis (H0) an
  ALTERNATIVE hypothesis (HA)
• Try to disprove H0
• There are 4 steps in hypothesis testing
• Identify the test statistic
• State the null and alternative hypotheses
• Identify the rejection region
• State your conclusion

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Session Outline

• Students t test.
• Frequency Data.
• Chi-square contingency tables.

4
Students t Test

• Normal distribution applies if s2 known
• When s2 unknown, can estimate by s2
• Bad news (xbar-m)/(s/?n) not N(0,1)
• Good news (xbar-m )/(s/?n) t(n-1)
• (n-1) is called the degrees of freedom

5
Performing Students t Test

• Do the patients in the C-section cohort have
  initial systolic BPs that are too low, i.e., less
  than 85 mmHg?
• STEP 1 Identify the T.S.
• T.S. x-barSBP-init

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Students t Distribution
t2.39
R.R.
-3s -2s -s 0 s 2s 3s
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Worked Example

• Do the patients in the C-section cohort have
  initial systolic BPs that are too low, i.e., less
  than 85 mmHg?
• STEP 2 State the hypotheses
• H0 ? ? 85 HA ? lt 85
• Note this is a one-sided test

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Worked Example

• Do the patients in the C-section cohort have
  initial systolic BPs that are too low, i.e., less
  than 85 mmHg?
• STEP 3 Identify the rejection region
• R.R. (x-barSBP-init 85)/(s/?n) lt t.05n-1

R.R. (80.25 85)/(5.877/?25) lt -2.06
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Worked Example

• Do the patients in the C-section cohort have
  initial systolic BPs that are too low, i.e., less
  than 85 mmHg?
• STEP 4 State your conclusion
• R.R. -4.04 lt -2.06 ? outside R.R.
• We reject H0. Data are consistent with initial
  systolic BPs that are too low.

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Frequency Data

• Not continuous, but counting
• Example (could be continuous)
• Instead of age in yearss
• patients with age gt 75 years
• Example (cant be continuous)
• Number of pregnant patients

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Frequency Data

• Can be expressed as a proportion
• Example 12 of 25 patients female
• Are distributed binomially b(n,p)
• Approximated by Normal distribution
• Can derive (Obs-Exp)2/Exp ?21

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Chi-square Contingency Tables
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Chi-square Contingency Tables
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H0 No effect of sex on stroke
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H0 No effect of sex on stroke
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Chi-square Contingency Table

• Calculated T.S. 0.568
• Rejection Region ?2.051 gt 3.84
• Cannot reject H0 (p0.451)

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Session Outline

• Students t test.
• Frequency Data.
• Chi-square contingency tables.

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Session Homework

• Drug X induces cancer remission in 35 of 50
  Asians and in 115 of 250 Caucasians.
• Does race affect the action of drug X?
• Use plt.05 for significance.
• Set-up using 4 steps of hypothesis testing.