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Reasoning in Psychology Using Statistics

- Psychology 138
- 2015

Exam 1(s)

Lab Ex1, mean 68.7/75 91.6

Lecture Ex1, mean 57.9/75 77.2

Combined (Lab Lecture) Ex1, mean 126.6/150

84.4

Descriptive statistics

- Summaries or pictures of the distribution
- Numeric descriptive statistics
- Shape modality, and skew (and kurtosis, not

cover much) - Measures of Center Mode, Median, Mean
- Measures of Variability (Spread) Range,

Inter-Quartile Range, Standard Deviation (

variance)

Measures of Center

- Useful to summarize or describe distribution with

single numerical value. - Value most representative of the entire

distribution, that is, of all of the individuals - Central Tendency 3 main measures
- Mean (M)
- Median (Mdn)
- Mode
- Note Average may refer to each of these three

measures, but it usually refers to Mean.

The Mean

- Most commonly used measure of center
- Arithmetic average
- Computing the mean

- Formula for population mean (a parameter)

- Formula for sample mean (a statistic)

M

The Mean

- Conceptualizing the mean

As the center of the distribution

As the representative score in the distribution

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

110 11 Mean 11/2 5.5

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

What happens if we add an observation to our

distribution?

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

What happens if we add an observation to our

distribution?

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

What happens if we add an observation to our

distribution?

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

What happens if we add an observation to our

distribution?

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

What happens if we add an observation to our

distribution?

1107 18 Mean 18/3 5.5

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

What happens if we add an observation to our

distribution?

1107 18 Mean 18/3

6.0

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

What happens if we add an observation to our

distribution?

1107 18 Mean 18/3 6.0

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

What happens if we add an observation to our

distribution?

1107 18 Mean 18/3 6.0

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

What happens if we add an observation to our

distribution?

1107 18 Mean 18/3 6.0

The Mean

- Conceptualizing the mean

As center of distribution

As the representative score in the distribution

To be fair, lets give everybody the same

amount.

1 2 3 4 5 6 7 8 9 10

119/7 17

1225306181513119

The Mean

- Conceptualizing the mean

As center of distribution

As representative score in distribution

Girl Scout bake sale for camping trip

1 2 3 4 5 6 7 8 9 10

17

17

17

17

17

17

17

119/7 17

1225306181513119

So everybody is represented by same score, the

mean is the standard

119/7 17

17171717171717119

A weighted mean

- Suppose that you combine 2 groups together.
- How do you compute new group mean?

Average the 2 averages

But it only works this way when the two groups

have exactly the same number of scores

A weighted mean

- Suppose that you combine 2 groups together.
- How do you compute new group mean?

205!? I only have 191

A weighted mean

- Suppose that you combine 2 groups together.
- How do you compute new group mean?

New Group

1225306181513251730191

Mean 191/10 19.1

12

30

6

13

30

18

17

25

25

15

A weighted mean

- Suppose that you combine 2 groups together.
- How do you compute new group mean?

The mean is the representative score in the

distribution

New Group

Characteristics of a mean

- Change/add/delete a given score, then the mean

will change.

Characteristics of a mean

- Change/add/delete a given score, then the mean

will change.

17

Characteristics of a mean

- Change/add/delete a given score, then the mean

will change.

16

Characteristics of a mean

- Change/add/delete a given score, then the mean

will change.

- Add/subtract a constant to each score, then the

mean will change by adding(subtracting) that

constant.

Characteristics of a mean

- Change/add/delete a given score, then the mean

will change.

- Add/subtract a constant to each score, then the

mean will change by adding(subtracting) that

constant.

- Multiply (or divide) each score by a constant,

then the mean will change by being multiplied by

that constant.

The median

- Median divides distribution in half 50 of

individuals in distribution have scores at or

below the median. - Case1 Odd number of scores

Step1 put scores in order

The median

- Median divides distribution in half 50 of

individuals in distribution have scores at or

below the median. - Case1 Odd number of scores

Step1 put scores in order

Step2 find middle score

The median

- Median divides distribution in half 50 of

individuals in distribution have scores at or

below the median.

- Case2 Even number of scores

Step1 put scores in order

Step2 find middle 2 scores

Step3 find arithmetic average of 2 middle scores

The mode

- Mode score or category with greatest frequency.
- Pick variable in frequency table or graph with

highest frequency (mode always a score on scale).

Mode

Modes

5

2, 8

Mode

Medium

Which center when?

- Depends on a number of factors, like scale of

measurement and shape. - The mean is the most preferred measure and it is

closely related to measures of variability - However, there are times when the mean is not the

appropriate measure.

Which center when?

- If data on nominal scale Mode only
- Unranked categories (e.g. eye color)
- Not a numeric scale
- Can not do arithmetic operations on values
- Can not calculate cumulative percentages

Which center when?

- If data on ordinal scale Median (plus Mode)
- Not a numeric scale (e.g., T-shirt size)
- Can not do arithmetic operations on values
- Can calculate cumulative percentages on

frequencies (median is score at 50th percentile)

Median of T-shirt size Medium Mode of T-shirt

size Medium

Which center when?

- If data on interval or ratio scale BUT
- Distributions open-ended
- Response category like 5 or more
- Extreme values unknown, so can not calculate mean
- Distributions skewed with long tails
- Extreme values over influence mean
- E.g., income sample of 50
- 47 middle income (60,000-100,000) and 3

millionaires or billionaires - Median 80,000
- Mean 135,000 or 60,000,000
- Median

(plus Mode)

Which center when?

- If data on interval or ratio scale AND no

exclusionary conditions Mean (plus Median) (plus

Mode) - Numeric scale
- Can do arithmetic calculations on values
- Have benefit of other statistics using the mean,

such as standard deviation

Which center when?

- Impact of shape on center (interval or ratio

scale)

Positively skewed distribution

Negatively skewed distribution

gt

gt

lt

lt

Mean median pulled toward tail

Chicago distributions

Mode 0-10,000

175-200,000 Median 45,734

261,600 Mean ?

325,212

Check out your hometown http//www.city-data.com

/

Buyer beware Know your distribution

The average price of houses in this neighborhood

is

Mode 0-10,000

175-200,000 Median 45,734

261,600 Mean ?

325,212

When you say average are you talking about the

median or the mean?

Wrap up

- Todays lab
- Compute mean, median, mode both by hand using

SPSS - Questions?