PS 366

4

Measurement

• Related to reliability, validity:

• Bias and error– Is something wrong with the instrument?

– Is something up with the thing being measured?

Measurement

• Bias & error with the instrument

– Random?

– Systematic?

Measurement

• Bias & error with the thing being measured

– Random?• failure to understand a survey question

– Systematic?• does person have something to hide?

Measurement

• Example:– Reliability, validity, error & bias in measuring

unemployment

– Census survey [also hiring reports, claims filed w/ government, state data to feds...]

– What sources of bias?

Measurement

• Unemployment [employment status]:

– Fully employed– Part time– looking for work, + part time– looking for work, no job– lost job, not looking for work– retired

Measurement

• Example: – Reliability, validity, error & bias in measuring

victims of violent crime

– Census surveys, police records, FBI UCR

– What sources of bias?

Measurement

• How do we ask people questions about attitudes, behavior that isn’t socially accepted?– prejudice– Racism– Feelings toward gays & lesbians– shoplifting

Measurement: Item Count Technique

• Here are 3 things that sometimes make people angry or upset. After reading these, record how many of them upset you. Not which ones, just how many?

• federal govt increasing the gas tax

• professional athletes getting million dollar salaries

• large corporations polluting the environment

Measurement: Item Count Technique

• federal govt increasing the gas tax

• professional athletes getting million dollar salaries

• large corporations polluting the environment

• federal govt increasing the gas tax

• professional athletes getting million dollar salaries

• large corporations polluting the environment

• a black family moving next door

Measurement: Item Count Technique

• Randomly assign ½ of subjects to the 3 item list

• Randomly assign ½ subjects to the 4 item list

• Difference in mean # of responses between groups = % upset by sensitive item– (mean 1 – mean 2) *100 = %

Item Count• Control TREATMENT

% upset

• Non South 2.28 2.24 0

• South 1.952.37 42

2.37 – 1.95 = 0.42 *100 = 42%

Item Count – Using poll information

• 1) The candidate graduated from a prestigious college

• 2) The candidate ran a business

• 3) The candidate’s family background

• 1) The candidate graduated from a prestigious college

• 2) The candidate ran a business

• 3) The candidate’s family background

• 4) The candidate is ahead in polls

Use poll info• Control TREATMENT % use poll

• All 2.28 1.36 1.39 3.2

• Young 1.04 1.46 41

• Is it significant?– Depends....how much does mean reflects the group?

How much variation around the mean?

Central Tendency: Chapter 4

• Statistics that describe the ‘average’ or ‘typical’ value of a variable

– Mean– Median– Mode

Central Tendency

• Why median vs. mean?

– Household income

– Home prices

Central Tendency

• Mean125 92 72126120 99130100sum=864

• mean = sum X/ N

• = 864 / 8

• mean = 108

• Is this representative?

Central Tendency

• Mean125 92300126120 99130100sum=1092

• mean = sum X/ N

• = 1092 / 8

• mean = 136.5

• Is this representative?

Central Tendency

• Mean130126125120100 99 92

• median = (N +1) /2– (8+1)/2– 9/2– 4.5 th – (120, 125)

• Is this representative?

Central Tendency

• Example$120,00$60,000$40,000$40,000$30,000$30,000$30,000

• Mean = $50,000 Mdn = $40,000 Mo = $30,000

• Which is most representative?

Mean vs Median

Mean vs. Median

• median = ½ point. 12.5 = 32,000

• mean = (Sum of X’s) / n = 816,000 / 25 = 32,640

Why is mean higher than median?

Normal vs. Skew Distributions

Which direction is skew here?

Frequency Distribution

Median vs Mean Price

• Seattle, 98121– Median $375,900– Mean $434,612

• Seattle, 98112 – Median $790,000– Mean $955,750

The Distribution

• Where is mean, median, mode if

– Normal

– Left / negative skew

– Right / positive skew

Normal vs. Skew Distributions

The Distribution

• Where is mean, median, mode if

– Normal ALL THE SAME

– Left / negative skew Mean less than median

– Right / positive skew Mean greater than median

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