College notes Introduction To Research Methodology - Pre-Master 's Social Research Methods, ISBN: 9780199689453

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