Data Analysis Quantitative Methods

1
Data Analysis (Quantitative Methods)

• Lecture 4

2
Dealing with Data

• Measurement Scales
• Descriptive Statistics
• Inferential Statistics

3
Levels of Measurement.

• Nominal Scale (Qualitative category membership
  e.g. gender, eye colour, nationality).
• Ordinal Scale (Ranks or assignments, positions in
  a group e.g. 1st 2nd 3rd).
• Interval and Ratio Scales (measured on an
  independent scale with units, e.g. I.Q scale.
  Ratio scale has an absolute zero point e.g.
  distance, Kelvin scale).

4
Discrete and Continuous

• Discrete Variables There are no possible values
  between adjacent units on the scale. For
  Example, number of children in a family.
• Continuous Variables Is a variable that
  theoretically can have an infinite number of
  values between adjacent units on the scale. For
  Example, Time, height, weight.

5
Descriptive Statistics
The purpose of descriptive statistics is to
organise and to summarise data so that it is more
readily comprehended

• Graphical Representation of Data
• Measures of Central Tendency
• Measures of Dispersion

6
Representing Data Graphically

• Bar Charts
• Histograms
• Pie Charts
• Scattergrams

7
The Bar Chart

• Used for Discrete variables
• Bars are separated

8
Histogram

• Columns can only represent frequencies.
• All categories represented.
• Columns are not spaced apart.

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Pie Chart

• Used to illustrate percentages

10
Scattergrams - Positive Relationships
11
Negative Correlation
12
No Relationship
13
Measures of Central Tendency

• The Mean
• The Median
• The Mode

14
The Mean
Mean Sum of all values in a group divided by
the number of values in that group. So if 5
people took 135, 109, 95, 121, 140 seconds to
solve an anagram, the mean time taken is
135 109 95 121 140
600 --------------------------------------------
----------- 120 5
5
15
The Mean Pros Cons

• Advantages
• Very Sensitive Measure.
• Forms the basis of most tests used in inferential
  statistics.

• Disadvantages
• Can be effected by outlying scores E.g.
• 135, 109, 95, 121,140 480. Mean 1080/6 180
  seconds.

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The Median
The median is the central value of a set of
numbers that are placed in numerical order.
For an odd set of numbers 95, 109, 121, 135, 140
The Median is 121
For an even set of numbers 95, 109, 121, 135,
140, 480 The Median is the two central scores
divided by 2. 121 135/2 128
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The Median Pros Cons

• Advantages
• Easier and quicker to calculate than the mean.
• Unaffected by extreme values.

• Disadvantages
• Doesnt take into account the exact values of
  each item
• If values are few it can be unrepresentative. E.G
• 2,3,5,98,112 the median is 5

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The Mode
The Mode The most frequently occurring value.
1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6,
7, 7, 7, 8
The Mode 5
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The Mode Pros cons

• Disadvantages
• Doesnt take into account the value of each item.
• Not useful for small sets of data

• Advantages
• shows the most important value of a set.
• Unaffected by extreme values

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Data Types and Central Tendency Measures.
The Mode may also be used on Ordinal and Interval
Data. The median may also be used on Interval
Data.
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Why look at dispersion?

• 17, 32, 34, 58, 69, 70, 98, 142
• Mean 65
• 61, 62, 64, 65, 65, 66, 68, 69
• Mean 65

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Measures of Dispersion

• The Range
• The Deviation Score
• The Standard Deviation

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The Range
The Range is the difference between the highest
and the lowest scores.
Range Highest score - lowest score
4, 10, 5, 12, 6, 14 Range 14 - 1 10
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The Deviation Score
Tells you how far away the raw score is from the
mean. The Deviation Score is calculated by
subtracting the mean score from each sample score
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An example
Raw Score Deviation score (raw score-mean) 2 2
- 6 -4 4 4 - 6 -2 6 6 - 6 0 8 8
-6 2 10 10 - 6 4 Total 30 Mean 30/56
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Raw scores and Deviation Scores
-4
4
-2
2
Raw Score
2
4
6
8
10
Mean
Deviation score
-4
-2
0
2
4
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Standard Deviation
The Standard Deviation is the average deviation
of the scores about the mean.
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Calculating the Standard Deviation
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Inferential Statistics

• Inferential statistics allows us to draw
  conclusions about populations, and to test
  research hypotheses.
• Inferential Statistics Involves
• Probability
• Statistical Tests e.g., t test and ANOVA

30
Summary

• All data is measured on either Nominal, Ordinal,
  Interval or Ratio Scales
• Variables can be discrete and continuos
• Descriptive Statistics such as measures of
  central tendency and dispersion are used to
  describe or characters data
• Inferential Statistics is used to make inferences
  from sample data about the population at large.