More statistics!

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Statement of proposal due today•Method section draft assigned

– Participants• Who will you survey or experiment on? What type of

sample?

– Procedures• If a survey, how conducted (individually, in groups?)

– Measures• How will you measure things?

More check in…

• Quiz next wednesday

• It will cover experimental design– Internal validity and threats– External validity and threats– Experiments and types of pilot studies– It will cover statistics through today

• Same format as last quiz

Today

• Frequency distributions

What is a frequency distribution

• Frequency– The rate at which a score on a variable occurs

in a sample

Frequency

Score Frequency

1, 1, 2

2, 2, 2, 3

3, 3, 3, 3 4

4, 4, 4, 4, 4 5

5, 5, 5, 5, 5, 5 6

6, 6, 6, 6, 6, 6 6

7, 7, 7, 7 4

8, 8, 8, 3

9, 9 2

Frequency distribution?

• How that frequency of scores is distributed or arranged

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9

Series2

Frequency distribution

• This is sometimes called a frequency polygon

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9

Series2

Types of frequency distributions

• The normal curve– Also called the Gaussian curve– The bell curve

• Describes how the data occur

• Their frequency

The normal curve

The normal curve?

• The rate of scores is symetrically distributed around the mean

• They follow a smooth increase/decrease with a peak at the mean, and frequencies of approximately 0 on either side

The normal distribution

• A lot of things are “normally” distributed

• Weight

• Height

• The normal distribution is important statistically– For reasons you don’t need to know right now

Other distributions?

• There are other important named statistical distributions—e.g. Poisson

• You don’t have to know them right now

• They are just different terms for talking about the way data are arranged

• Data—a plural term

A lot of data is not normally distributed

• It is skewed

• When data are “skewed” there are a lot more scores on one side than the other

• Income is a fine example

• It is positively skewed

• There are more scores on the “left” side of the distribution

Positive skew

0

200

400

600

800

1000

1200

1 2 3 4 5 6 7 8 9

Series2

Positive Skew

• Measures of mental illness symptoms like depression are usually positively skewed

• Most people don’t have many symptoms

0

200

400

600

800

1000

1200

1 2 3 4 5 6 7 8 9

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Negative skew

• When there is more data on the right hand side of the distribution

0

100

200

300

400

500

600

1 2 3 4 5 6 7 8 9

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Why is the normal distribution special?

• We can make probability statements about the occurrence of certain scores– If the data are normally distributed