Basics of quantitative methodology
E2040 Week 4
2024

Study objectives
•At the end of this lesson, student will be able to:
1.Understand the basics of quantitative methodology
2.List basic types of variables
3.Know basic types of data visualization
4.Know basic types of summary statistics

Types of variables



Categorical variables
•Nominal – qualitative values, no ordering
•sex, ethnicity, birth month
•Binary/dichotomous – two categories
•No/yes, dead/alive, case/control
•
•Ordinal – have several ordered categories
•Level of education (elementary, high school, college), Likert scale ([1]strongly disagree –
strongly agree[5])
•

Continuous variables
•Can take any value within a range
•Theoretically infinite values
•
•Examples: blood pressure, height, temperature, liquid volume

KvIS 1



Distribution
A graph of a price Description automatically generated with medium confidence
•How data values are spread across different values
•Normal distribution – Gaussian, symmetrical
•Skewed distribution
•Positively skewed (right-skewed), negatively skewed (left-skewed)
•Bimodal distribution
•

Normal/Gaussian distribution



Galton board and the laws of nature
•

https://www.edumedia-sciences.com/en/media/905-galton-board

Measures of central tendency
1.Mean – the average value (sum of values / number of values)
2.Median – the value in the middle of distribution (50th percentile)
3.Mode – the most frequent value
•

Measures of central tendency
•
A diagram of a function Description automatically generated

•Skewness
•
•
•
•Kurtosis
Non-normal distributions

•



KvIS 2



Measures of spread
•How spread our data are around the central tendency
•The lower the spread, the more representative the measures of central tendency are of the data
•High spread = large variability

Standard deviation (SD)
•Amount of variation of the values from the mean
•High SD = high variability
•
•(population SD): square root of the mean of squared differences of individual values from the mean
= variance
•Sample SD = using n-1 instead of N




Basic descriptive terms
•Sum – adding values together
•Mean (M) – sum of values divided by their count
•Mode – most frequently occurring value
•Median – value at the 50% (“in the middle”)
•Standard deviation (SD) – distance of a value from a sample mean
•Variance – squared SD
•Quantile – cut point dividing the range of the distribution into intervals with equal
probabilities
•Minimum – the smallest value
•Maximum – the largest value
•

Visualizing the distribution
A graph of a number of colored bars Description automatically generated with medium confidence A
graph of different colored bars Description automatically generated A graph with different colored
boxes Description automatically generated A pie chart with different colored bars Description
automatically generated

Pie chart
•Categorical variables
•Visualizing the proportions of values
•Typically as a percentage
A pie chart with different colored bars Description automatically generated

Bar chart
•Categorical variables
•Frequency of  values for each category
•
A graph of different colored bars Description automatically generated

Boxplot
•Continuous variables
•Illustrates the spread of values
•Median, percentiles, min/max
•Outliers
•
•
A graph with different colored boxes Description automatically generated




Histogram
•Continuous variables
•Values are divided into bins = range of values
•Visualizing the density
•
•
•Bars in histogram vs bars in bar chart
•Different range of values vs different categories
A graph of a number of colored bars Description automatically generated with medium confidence

Scatterplot
•Two continuous variables
•Bivariate distribution
•
•
A diagram of a happiness score Description automatically generated

•



KvIS 3



Data cleaning
•Data often contain errors, missing values, outliers
•
•This might be due to
•Contamination (biological samples)
•Error in data entry
•Just a really atypical case (with regards to outliers)

Outliers
•atypical data point with regards to sample values
•Example
•Erasmus students in class – 10 students
•
•With outlier:
•M = 25.8
•SD = 15.9
•Median = 21
•
•Without outlier:
•M = 20.8
•SD = 0.83
•Median = 21
•
•
•
•
#
age
1
20
2
21
3
20
4
22
5
21
6
20
7
22
8
20
9
71
10
21

Identifying outliers – graphs
Box plot with 1.5 IQR = everything beyond that is outlier
symmetric with outlier histogram

Outliers – what should we do?
•Errors in data entry – need to fix
•Extreme values
•Remove?
•Keep in?
•Substitute?
•Transform?
•Depends on the type of data
•

Outliers?
Yang, S., Puggioni, G., Harlow, L. L., & Redding, C. A. (2017). A Comparison of Different Methods
of Zero-Inflated Data Analysis and an Application in Health Surveys. JMASM Editors, 16(1), 518-543.

Missing data
A white puzzle with a missing piece Description automatically generated
•Missing data – no response for some or all of variables for an individual
•Missing data can lead to biased results
•
•Handling missing data
•Poor handling:
•Listwise deletion
•Pairwise deletion
•Mean/median imputation
•Good handling:
•Multiple imputation
•Full information maximum likelihood
•

Multiple imputation
Nissen, J., Donatello, R., & Van Dusen, B. (2019). Missing data and bias in physics education
research: A case for using multiple imputation. Physical Review Physics Education Research, 15(2),
020106.