6. MTB Step 3 - Standard Error of the Mean

Question 1

STANDARD ERROR OF THE MEAN (SEM)

What does SEM Measure and How is it Calculated?

Answer 1

• SEM is a measure of how tightly grouped a set of data is. The lower-case Greek letter σ (sigma) stands for SD.
• SEM is the SD divided by the square root of the number of samples, or n , as shown in the following equation:

SEM = σ_x = σ / sqrt of n

Question 3

STANDARD ERROR OF THE MEAN (SEM)

Given the Equation for SEM, what happens to the Dataset Grouping as the Sample Size (n) gets Larger?

Answer 3

The Grouping becomes Narrower = More Precise

Question 4

Z-SCORE

What does the Z-Score show you and what is the Equation?

Answer 4

Z-Score shows how far ABOVE or BELOW your score is compared with the Mean score.

Z-Score = (Score - Mean) / SD

Question 5

Z-SCORE

If the USMLE Step 3 has a mean score of 222 and a Standard Deviation (SD) of 16, what are the Z-Scores for the following?:

1. If you score a 238
2. If you score a 206
3. If you score a 234

Answer 5

• If your score is 238
  
  • (238 - 222) / 16 = +1SD Above Mean
  • Z-Score = +1.0
• If your score is 206
  
  • (206 - 222) / 16 = -1SD Below Mean
  • Z-Score = -1.0​​
• If your score is 234
  
  • (234 - 222) / 16 = 12 / 16 = +0.75SD Above Mean
  • Z-Score = +0.75

Question 6

CONFIDENCE INTERVAL (CI)

What does the Confidence Interval (CI) give an indication of?

Answer 6

Confidence Intervals give an indication of How Precise a given collection of data is:

• Are data points Centralized around the Mean, or are they Scattered?
  
  • More Scattered = Less Precise

Question 7

CONFIDENCE INTERVAL (CI)

What does it mean when the Outcome has a Confidence Interval (CI) that crosses 1.0?

Answer 7

Results NOT significant

Question 8

CONFIDENCE INTERVAL (CI)

What is the association between the Confidence Interval and the Standard Error of the Mean (SEM)?

Answer 8

The 95% Confidence Interval (CI) is basically 2-times the Standard Error of the Mean (SEM).

• If 95% CI = 2 x SEM
• and SEM = SD / sqrt n

Then, to double the CI (precision) you have to Quadruple the sample size (n)

• Let’s say you have a 95 percent CI of 4–8 with a mean of 6. This means 95 percent of measures are between 4 and 8. If you want to tighten this range and cut the CI in half to a range of 5–7, you would need to take four times the number of measurements. Both data groups have a mean of 6. The one with the narrower 95 percent CI is more precise.

Question 9

CONFIDENCE INTERVAL (CI)

Explain the following situation:

“Suppose that a drug to prevent a stroke from atrial fibrillation has a mean benefit of 30 percent relative risk (RR) reduction in stroke with a value of 0.7. This looks like a good drug. However, If the CI is listed as 0.5 to 1.5, this study had no validity.

Why?

Answer 9

These measures may mean that the:

• Average patient had a 30 percent reduction in the risk of Stroke (RR = 0.7)
• Some patients had a 50 percent increase in the risk of Stroke as well (RR 1.5).
• When the CI crosses 1.0, it means the results are not precise enough to be useful.

Question 11

STANDARD ERROR OF THE MEAN (SEM)

What does overlapping Standard Error of Measurement Error bars represent?

Answer 11

A Non-statistically significant difference (no sign. diff.)