Flashcards in The normal Distribution + Z-scores Deck (14)

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1

## What is the normal distribution curve?

###
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

2

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

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- the relative frq of observations

- to the probability of observations

3

## How are probabilities expressed?

### - p-values between 0 - 1

4

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

### - the SD cuts off a constant proportion of the distribution

5

## What are z-score?

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- 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

6

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

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- 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

7

## Why use z-scores?

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- 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

8

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

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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)

9

## how can we use the logic behind z-score?

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

10

## What are some problems of using z-score?

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

11

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

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- Null hypothesis significant testing

- "innocent until proven guilty"

12

## What is the central limit theorem?

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= 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

13

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

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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)

14