This brief (samenvatting) is meant for TU/e students enrolled in the course 2DBM90 Applied Biostatistical Modelling. This brief is very complete, encompassing all lectures and slides as well as the relevant chapters in the recommended book "Learning statistics with jamovi". Brief is fully in Englis...
• N: the number of observations.
• Xi : the label of one observation.
• X̄: the mean.
• Mode: the mode of a sample is the value that occurs the most. Often calculated when
you have nominal data, because the mean and median are useless for those sorts of
variables.
Types of Data
There are two categories of data: Categorical (nominal and ordinal) and Continuous (scale
and numerics) data.
Measures of variability
• Range: difference between highest and lowest value. Can be robust or not (check
outliers). Full spread of the data, very vulnerable to outliers.
• Interquartile range: Difference between the 25th percentile and the 75th percentile of
the data. Middle half of data, pretty robust.
• Average Absolute Deviation: distance from mean: |Xi − X̄| divided by n.
• Variance: Squared variations are better than absolute variations, therefore we use the
variance: s2 . With formula V ar(X) = N1 N 2
i=1 (Xi − X̄) . Jamovi is using a slightly
P
different equation: N1−1 N 2
i=1 (Xi − X̄) .
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• Standard Deviation: the square root q of the variance. This is also called the Root Mean
1 PN
Squared Deviation (RMSD): σ̂ = N −1 i=1 (Xi − X̄)2 . Rule of thumb: expect 68%
of the data to fall into 1 sd, 95% into 2 sd and 99.7% to fall into 3 sd. Is expressed in
the same units as the data. Most popular measure of variation.
4
,CHAPTER 4. DESCRIPTIVE STATISTICS 5
Standardized Scores
Describe a variable in terms of the overall distribution. You can calculated the standard
score, that is describe a variable in how much std’s it lays from the mean: zi = Xiσ̂−X̄ . Than
you can convert that to percentages with the rule of thumb or with tables. This is relative
to its own population. BUT it is possible to compare standardized scores across completely
different variables.
4.1 Exploratory Data Analysis
Data Remarks
Sample Size N Adequate? Small?
Location Mean, Median
Extremes Min, Max
Disperity SD, IQR
Symmetry Reasonable? Doubts? Check boxplot for differences in quartile
Normality Reasonable? Concerns? QQ-plot, Shapiro-Wilk’s p
Outliers Case #..
Others Small sample size? Therefore....
,Chapter 5
Drawing graphs
• Histogram: for interval or ratio scale.
• Boxplot: Used for getting the IQR.
• Stripchart: Is preffered over boxplot when N is small (<14).
• Violin plot: Similar to boxplot, but also show kernel probability density.
• Scatterplot: Direction, Form, Strength, Unusual features? Used to check for correla-
tion.
• QQ-plot: Checks for normality, data is normal if the QQ-plot approximates a straight
line.
You should always check for center, dispersion, symmetry and outliers.
6
, Chapter 6
Pragmatic matters
6.1 Contingency tables
The contingency table shows a table of raw frequencies. That is, a count of the total number
of cases for different combinations of levels of the specified variables. However, often you
want your data to be organised in terms of percentages as well as counts.
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