The normal Distribution + Z-scores

Question 1

What is the normal distribution curve?

Answer 1

is a mathematical abstraction which conveniently describes (“models”) many frq distributions of score in rl
- area under the curve is directly proportional to… the relative frq of observations

Question 2

The area under the normal distribution curve is directly proportional to….

Answer 2

• the relative frq of observations

- to the probability of observations

Question 3

How are probabilities expressed?

Answer 3

• p-values between 0 - 1

Question 4

What is the relationship like between the normal curve and the SD?

Answer 4

• the SD cuts off a constant proportion of the distribution

Question 5

What are z-score?

Answer 5

• standard sores
• states the position of a raw score in relation to the mean of the distribution using SD as the unit of measurement
• (raw score - mean)/SD

Question 6

What does the size of the SD tell us about the value of z?

Answer 6

• bigger the SD the more scores are spread out around the mean
• If SD small, a score that is even slightly different from the mean is unusual
• If the SD is large, a score has to be very different from the mean in order to be unusual

Question 7

Why use z-scores?

Answer 7

• make it easier to compare score from distributions using different scale
• Enables us to determine the relationship between one score and the rest of the scores, using just one table for all normal distributions (the whole working out bit which we don’t need for the exam)
• can be used to define a “cut-off” point in a test

Question 8

What are statical logic tests which underlie the logic of z-scores?

Answer 8

1. Scores are normally distributed around their mean
2. Sample means are normally distributed around the population mean
3. Differences between sample means are normally distributed around zero (no difference)

Question 9

how can we use the logic behind z-score?

Answer 9

• help decide whether or not an observed difference between sample means is due to chance

Question 10

What are some problems of using z-score?

Answer 10

• difference between groups may be due to a fluke? change (sample variation) or NOT due to chance

Question 11

What is the best way to deal with the problem of using z-score?

Answer 11

• Null hypothesis significant testing

- “innocent until proven guilty”

Question 12

What is the central limit theorem?

Answer 12

= sample means tend to be normally distributed around the population mean, regardless of the actual shape of the population itself
- if you plot the frq with which each sample mean occurs = normal distribution curve

Question 13

What is the difference between type 1 and type 2 errors?

Answer 13

Type 1 error: False positive
- rejected null, when should’ve accepted it (there was no significant difference)
Type 2 error: False negative
- accepted null, when should’ve rejected (there was significant difference)

Question 14

What does the 0.05 significance level mean?

Answer 14

• comprimise between the risk of making a type 1 or type 2 error
• set probability of making a type 1 error at 0.05 and considered as “real”, the difference