1 Descriptive statistics: Measures of dispersion Mary Christopoulou Practical Psychology 1 Lecture...

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1 Descriptive statistics: Measures of dispersion Mary Christopoulou Practical Psychology 1 Lecture 3

Transcript of 1 Descriptive statistics: Measures of dispersion Mary Christopoulou Practical Psychology 1 Lecture...

Page 1: 1 Descriptive statistics: Measures of dispersion Mary Christopoulou Practical Psychology 1 Lecture 3.

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Descriptive statistics:

Measures of dispersion

Mary Christopoulou

Practical Psychology 1 Lecture 3

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Key terms

Standard Deviation= τυπική / “σταθερή”

απόκλιση από τον μέσο όρο

Variance/ variability = Διακύμανση

Range = Εύρος

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Descriptive statistics:

statistical measures that summarize and

communicate the basic characteristics

of a distribution

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2 Types of Descriptive Statistics

Measures of central tendency:measures that communicate the degree to

which scores are centred in a distribution

Measures of dispersion:measures that communicate the degree to

which scores are spread out in a

distribution

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Measures of

central tendency Mean

Median

Mode

Measures of

dispersion Range Interquartile range Variance Standard Deviation

2 Types of Descriptive Statistics

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Measures of dispersion

They show: how far from the center the data tend to

range/ spread. the extent to which scores in a distribution

differ from each other How large are the differences between

individual scores? How much variability is there in the data?

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An example

N of chocolate cookies consumed by 10 girls and 10 boys:

Girls = 5, 3, 9, 12, 10, 12, 4, 9, 7, 2 (mean = 7.3) Boys = 6, 7, 7, 8, 8, 8, 7, 7, 8, 7 (mean = 7.3)

Which of the two means is a more accurate reflection of underlying data? 2 issues:

consistency of data: smaller amount of variability indicates a greater consistency of the data (and vice versa)

Accuracy/reliability of measure of central tendency

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Example cntd…

Girls = 5, 3, 9, 12, 10, 12, 4, 9, 7, 2 (mean = 7.3)

Boys = 6, 7, 7, 8, 8, 8,7, 7, 8, 7 (mean = 7.3)

Girls’ mean is based on scores with greater variability,

and Boys’ mean is based on scores with smaller

variability.

Mean for Boys is a more accurate reflection of

underlying data, as it is based on a sample that is

more consistent (from one score to the next).

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Range

Range is the difference (distance)

between the highest and lowest value

in the data

Can be calculated for all levels of

measurement, apart from the nominal

level.

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RANGE example

RANGE = 9 - 1 = 8

1 2 3 4 52 7 9

3, 2, 4, 9, 5, 7, 1, 2

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How to calculate the range

1. Put scores from lowest through highest2. Find the highest value and the lowest

value of the data set 3. Subtract the lowest score from the

highest score

Example: 22, 25, 30, 42, 88, 102Range is 102 – 22 = 80

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Range

Used as a very quick (“rough”) method

Quite inefficient – only the smallest and

largest values are used

Excessively vulnerable to outliers

(extreme scores)

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Inter Quartile Range

The IQR (Inter Quartile Range) is not affected by extreme scores

Divide the data into 4 equal parts (Quartiles)

delete the extreme quarters of data and measure range of middle 50%

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28 2 4 1 5 2 7

How to find the IQR:1. Put scores in order 2. Delete the extreme quartiles

1 2 2 4 5 7 28

IQR= 5 - 2 = 3

3

3

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Variance and Standard Deviation

Two measures of variability that tell us how much scores are spread around a mean.

Note: a mean of 50 could indicate that most

scores are between 48-52, or could indicate

that most scores are between 40 and 80!!

48 - - - 52

40 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 80

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Variance (or Variability)

It is the degree to which scores are spread

around the mean

It involves the average square deviation of

each value from the mean of the values

It is the average error between the mean and the

observations made.

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Example Which set of scores are more spread out?

Set A: 40, 40, 50, 60, 60 mean=50

Set B: 40, 49, 50, 51, 60 mean=50

40 50 60

40 60

40 50 60

49 51

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If we subtract each score from its group

mean we can see that:

4 of the scores in set A are 10 units away from

the mean,

whereas only 2 scores in set B are 10 units

from the mean.

Thus A has the greater variance!!

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Variance

The most efficient of the measures of dispersion

Only valid for interval & ratio scales

Vulnerable to outliers

The larger the value of the Variance, the more

each score is “distant” from the mean.

The smaller the Variance, the closer each score

is, to the mean.

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The Standard Deviation (SD)

Recall that calculation of the Variance involves squaring the deviation scores.

This means the Variance value is much larger than the actual deviation of scores from the mean.

Therefore, the variance value is not reported often.

Instead, report the Standard Deviation.

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Standard Deviation

Is the average amount by which scores in a

distribution differ from the mean Shows the

average distance of the data from the mean

It is a measure of how well the mean

represents the data.

Is a measure of the degree of dispersion of

the data from the mean.

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Interpreting SD…

large SD = scores are far from the mean (so, the mean is not an accurate representation of the data).

small SD = scores are closer to the mean (scores are more

clustered around the mean).

E.g. 3 data sets, each has an average of 7.

1. 0, 0, 14, 14 SD = 7

2. 0, 6, 8, 14 SD = 5

3. 6, 6, 8, 8 SD = 1

The 3rd set has a much smaller standard deviation than

the other 2 because its values are all close to 7.

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Interpreting SD using our example…

Recall that mean = 5, SD = 2.00 in our example

“Boundary at minus one SD” = 5 - 2 = 3 “Boundary at plus one SD” = 5 + 2 = 7 These boundaries indicate how much scores

are spread around the mean. Thus, the majority of scores in our sample are

between 3 and 7 (this is true)

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Important!

In scientific reports (including your lab write-ups) it is important to report both a measure of central tendency and a measure of dispersion

Mean & SD for normally distributed data Median & IQR for skewed data

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Reporting Results APA format

Q. what is the mean and standard deviation? A. (M = 5.00, SD = 2.00).

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Small Revision

Descriptive Statistics

Measures of Central Tendency

Measures of Dispersion

Range

Interquartile Range

Variance

Standard Deviation