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College notes Introduction To Research Methodology - Pre-Master 's Social Research Methods, ISBN: 9780199689453
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Exam Review (Statistics)Big Picture
1. Descriptive and univariate statistics show minor info regarding samples (dispersion,
mean…)
2. Bivariate Statistics focus on viewing if relations between variables is present
3. T-test & ANOVA focus on seeing if effects of a given variable are the same among different
groups
Notes
Univariate Statistics (focus on one variable and its properties)
Measurement Levels
o Nominal
Basic distinction between categories
Categorical Eg: religions, sex, colors…
o Ordinal
Distinction between categories and ranking of value
Eg: Low-medium-high, top 5 favorite food…
o Interval
Distinction between categories, ranking of value and equal sized
intervals
Eg: Temperature in Celsius, age in years, population, hours spent,
Continuous income…
o Ratio
Distinction between categories, ranking value, equal sized intervals
and natural zero point
Eg: time, temperature in Kelvin
Describing Frequencies
o Describing Frequencies may be very simple in certain cases, in others
however, it is necessary to rely on proportions to create a reasonable
comparison
Frequency
Proportion=( )∗100
Number of samples
F
P=( )∗100
N
2016-2017 2017-2018
W Europe 6 12
N America 10 9
Total 16 21
Eg: Origin of Pre-Maters students
6
PWE = ( )
16
∗100=37.5 %
Describing Distribution
o Mode
Category with most observed subjects
Eg: W. Europe 2017-18
, o Median
Middle value after numbers are ranked in increasing order
Requires ordinal measurement level at minimum
Odd numbers just pick middle number
Eg: 6,9,10,12,14
Median= 10
Even numbers, simply add the two middle numbers and divide by 2
Eg: 6,9,10,12
(9+10)/2=(19)/2=9.5
o Mean
Arithmetic average of all samples
Requires interval or ratio level variables
Formula
of all sample results
Mean= ∑
Number of samples
Σx
M=
N
o Range
Indicates the difference between the lowest score and highest score
Formula
Range=x −X
o Interquartile Range
Similar to range but focuses on values within the 75% and 25%
quartiles
Formula
IR=Highest qvalue (75 %)−Lowest qvalue( 25 %)
Measure of Dispersion When to use it
Mode Nominal measurement levels
Median Ordinal measurement levels
Mean Interval/Ratio measurement levels
Deviations from mean
o Deviance
How far is a given variable from the mean
Formula
Deviance=variable−mean
D=x i−x
o Variance
How close around the mean is the data (same as standard deviation)
Formula
for each variable :( variable−mean)then add all of them up
Variance=
Number of Samples−1
2 Σ( x i−x )
σ =
N−1
o Standard deviation
Similar to variance but expressed in a scale compatible with variables
, Grants some indication of how data is dispersed
Formula
each variable :(variable−mean)then add all of them up
Stand . Dev .=√
Number of Samples−1
Σ(x i−x )
σ =√
N −1
o Degrees of Freedom
Indicate how many variables are present, each time one is used a
degree of freedom is lost
Scores & Standardization
Types of distribution
o Skew
Positive
Negative
o Kurtosis
Leptokurtic (+2.6)
Platykurtic (-0.9)
o Bimodal distribution
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