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Reasoning in Psychology Using Statistics

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Title: Social Science Reasoning Using Statistics Author: Psychology Department Last modified by: Admin Created Date: 1/31/2011 2:09:48 PM Document presentation format – PowerPoint PPT presentation

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Title: Reasoning in Psychology Using Statistics


1
Reasoning in Psychology Using Statistics
  • Psychology 138
  • 2015

2
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
3
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)

4
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.

5
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
6
The Mean
  • Conceptualizing the mean

As the center of the distribution
As the representative score in the distribution
7
The Mean
  • Conceptualizing the mean

As center of distribution
As representative score in distribution
8
The Mean
  • Conceptualizing the mean

As center of distribution
As representative score in distribution
9
The Mean
  • Conceptualizing the mean

As center of distribution
As representative score in distribution
10
The Mean
  • Conceptualizing the mean

As center of distribution
As representative score in distribution
11
The Mean
  • Conceptualizing the mean

As center of distribution
As representative score in distribution
110 11 Mean 11/2 5.5
12
The Mean
  • Conceptualizing the mean

As center of distribution
As representative score in distribution
13
The Mean
  • Conceptualizing the mean

As center of distribution
As representative score in distribution
What happens if we add an observation to our
distribution?
14
The Mean
  • Conceptualizing the mean

As center of distribution
As representative score in distribution
What happens if we add an observation to our
distribution?
15
The Mean
  • Conceptualizing the mean

As center of distribution
As representative score in distribution
What happens if we add an observation to our
distribution?
16
The Mean
  • Conceptualizing the mean

As center of distribution
As representative score in distribution
What happens if we add an observation to our
distribution?
17
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
18
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
19
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
20
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
21
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
22
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
23
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
24
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
25
A weighted mean
  • Suppose that you combine 2 groups together.
  • How do you compute new group mean?

205!? I only have 191
26
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
27
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
28
Characteristics of a mean
  • Change/add/delete a given score, then the mean
    will change.

29
Characteristics of a mean
  • Change/add/delete a given score, then the mean
    will change.

17
30
Characteristics of a mean
  • Change/add/delete a given score, then the mean
    will change.

16
31
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.

32
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.

33
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
34
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
35
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
36
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
37
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.

38
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

39
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
40
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)
41
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

42
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
43
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
/
44
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?
45
Wrap up
  • Todays lab
  • Compute mean, median, mode both by hand using
    SPSS
  • Questions?
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