Transcript Introduction to Quantitative Methods

Quantitative Methods
Part 1
Intro to Statistics
Descriptive and Inferential Statistics

Descriptive
◦ Relies only on data you
have collected
◦ Uses simple graphic
analysis and simple
summation of the data
including the sample and
the measures.
◦ Basic feature of the data

Inferential
◦ Used to infer about
properties/parameters
of a population
◦ Extends beyond the
immediate data you have
collected
◦ Investigates models and
hypothesis
Descriptive Statistics
Looks at a single variable and tends to hone
on 3 main things
Distribution
 Central tendency
 Dispersion

Distribution
Shows frequency of individual or a range
of values
 Can be grouped into categories
 Can use percentages
 Shown in frequency table or chart

Frequency Table and Chart
Central Tendency
Shows distribution of a central value
 Uses Mean, Median and Mode

◦ Mean = Average
◦ Median = Middle number (sorted)
 If even numbers then add the 2 middle and divide
by 2
◦ Mode = The one that appears the most
Central Tendency (2)
9 people earn £10,000
 1 earns £11000


Work out the Mean, Median and Mode

What does this tell us?
Dispersion

Measures the spread of values around the
central tendency (to see the variability of
sample and how well the mean represents
our data)

Some methods of measuring spread are
◦ Range
◦ Quartiles
◦ Standard Deviation
Range
(Measure of Spread)
Simplest of them
 Range = Maximum – Minimum

Quartiles
(Measure of Spread)
Breaks it into quarters
 25th percentile (1/4) Shows 25% of the lower data values
 50th percentile is the middle
 75th percentile (3/4) Shows 25% of the higher data values

Quartile Example

Shoe-size data collected from a sample of
UW boys and girls (Dr C. Price’s
workshop 4)
Girls shoe size:
444444455555555666677778

Quartile Example (Cont)
Girls shoe size:
444444455555555666677778
 25th percentile (1/4 of 24 =6)

◦ 6th data value = size 4

75th percentile (3/4 of 24 = 18)
◦ 18th data value = size 6
However useful if you need something that takes
into account all the scores/data you need......
Standard Deviation

Measures the spread of scores within the
data set
◦ Population standard deviation is used when
you are only interested in your own data
◦ Sample standard deviation is used when you
want to generalise for the rest of the
population
Standard Deviation

Sigma s = SD
Mu
m = Mean
× = Data Value
S = Sum
N = Number of data
SS = Sum of the Squares
To find the standard deviation
◦
◦
◦
◦
Calculate the deviation from mean (x – m )
Square this (x – m ) * (x – m )
Add all squared deviation (S) = SS
SD ( s ) = Square Root of SS / N
Standard Deviation
Workshop
Please ensure that you do Workshop 3
and then work on Workshop 4
 Your initial Gantt chart
 Your journal and Lit Review (Homework)

References




Dr C. Price’s notes 2010
http://statistics.laerd.com/statistical-guides/descriptive-inferentialstatistics.php
http://www.socialresearchmethods.net/kb/
Gravetter, F. and Wallnau, L. (2003) Statistics for the Behavioral
Sciences, New York: West Publishing Company