7. MTB Step 3 - Z-score, CIs, Correlation Coefficient, T-score, ANOVA, Chi-square

Question 1

Z-SCORE

Explain the Concept and Application of the Z-Score?

Answer 1

A way of showing how far Above or Below your score is compared with the Mean:

Z-Score = (Your Score - Mean) / SD

• 1 SD Above Mean: Z-Score = +1.0
• 2 SD Above Mean: Z-Score = +2.0

Example:

Given: Mean = 240 and SD = 18, what is Z-Score for a score of 254?

Z-Score = 14/18 = +0.78

Question 2

CONFIDENCE INTERVALS (CIs)

What do Confidence Intervals (CIs) give an indication of about a collection of data?

Answer 2

CIs give an indication of HOW PRECISE a given collection of data is.

• Are the data points Centralized around the Mean, or are they Scattered?
• The greater the Scatter, the less the Precision

Question 3

CONFIDENCE INTERVALS (CIs)

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

Answer 3

Results are NOT Significant

Question 4

CONFIDENCE INTERVALS (CIs)

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

Answer 4

The 95% CI = 2 x SEM

• Since SEM = SD / sqrt n
• In order to Double the Precision of a test you need to Increase the sample size (n) by 4 times
  
  • ​Say you have a 95% CI of 4-8 with a Mean = 6. This means 95% of measures are between 4 and 8.
  • If you want to tighten this rand and cut the CI in half to a range of 5-7, you would need to take 4 x n.
  • Both data groups have a mean of 6 but the one with the Narrower 95% CI is More Precise.

Question 5

CORRELATION COEFFICIENT (r)

What is the Correlation Coefficient (r)?

Answer 5

The Correlation Coefficient (r) is what you use to give a Numerical Value to the level of connection or correlation between Two Variables or Two Groups.

• Very Strong Correlation = +1
• Strong Inverse Correlation = -1
• No Correlation = 0

Question 6

T-SCORE

Explain the Concept and Application of the T-Score (a.k.a. T-Test).

Answer 6

1. Used to assess TWO groups of data.
2. Can analyze samples that are NOT in a normal distribution.
3. When you only have a sample of measurements of the entire population.

• Example:*
• Measuring the lead levels in water supplies from TWO different outlets throughout the city.*
• “What are the Differences between the two groups?”*

Question 7

CHI-SQUARE

Explain the Concept and Application of a Chi-Square.

Answer 7

Compares multiple groups AND indicates whether or not they are Statistically DIFFERENT.

“Are the groups DIFFERENT or not?”

Question 8

ANALYSIS OF VARIANCE (ANOVA)

Explain the Concept and Application of an Analysis of Variance (ANOVA).

Answer 8

1. Used to assess ≥​ 3 groups of data.
2. Can analyze samples that are NOT in a normal distribution.
3. When you only have a sample of measurements of the entire population.

• Example:*
• Measuring the lead levels in water supplies from THREE + different outlets throughout the city.*
• “What are the Differences?”*