Module 5, Normal Distributions

Question 1

z-scores may be interpreted by:

Answer 1

1. a score’s distance from the mean
   * z-scores indicate distance from the mean is standard deviation units
   * transform them into z-scores to compare two different normal distributions
2. a score’s location relative to the entire distribution

Question 2

Standardizing Frequency Distributions

Answer 2

standardized scores:
- used to compare and combine scores that come from different distributions
- when you change a score in its raw to a z-score we call standardizing a score
example:
imagine you want to compare your recent score of 80 on your statistics exam to your roommate’s score of 75 on a exercise physiology exam
◦ scores from different classes
with different distributions are
not directly comparable
◦ 2 different distribution of
scores (could have different
means and different SD) units
are the same (%)

Question 3

Does the Distribution Change Shape? (standardizing it)

Answer 3

• standardizing distributions does not change the shape of the distribution
  
  • it is a linear transformation
• ex. transforming temperatures in fahrenheit to celcius

Question 4

Normal Distribution

Answer 4

• a distribution based on a population of an infinite number of scores
• generated from mathematical formulas
  ◦ not collected data (unlike
  frequency distribution)

Question 5

Characteristics of a Normal Distribution

Answer 5

1. the left and right tails continue to infinity without touching the x-axis (since they are generated from mathematical formulas there is an infinite amount)
2. shape (“bell-shaped”):
   A. unimodal
   B. symmetric (left half is mirror
   image of right half)
3. the mean is the population mean (μ)
4. the standard deviation is the population standard deviation (σ)

Question 6

Why do we care about Normal Distributions?!

Answer 6

• researchers believe that many variables are normally distributed
• many inferential tests are based mathematically on the assumption of normal distributions
• we can determine the proportion of the distribution associated with any given score

Question 7

Problem with Normal Distribution

Answer 7

• distributions with the same population standard deviation but with different population means
• distributions with the same population means but different population standard deviations
• different units of measurement, distributions can have different means and different standard deviations (different amounts of variability) - cannot compare scores from two different normal distributions however when we want to compare we want to use standard normal distribution

Question 8

Standard Normal Distribution

Answer 8

to avoid confusion that may come from different units of measurement, researchers use the standard normal distribution

z-scores are measured in standard deviation units
- number of deviations from the mean
mean is always 0
standard deviation is equal to 1
symmetric, unimodal and mesokurtic based on mathematical formula