Summary of Frequent Statistics (SOW-BKI138) course material, based on book "Introductory Statistics with Randomization and Simulation" by OpenIntro. This course is part of the AI bachelor curriculum, taught by Radboud University.
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topic 1: introduction to statistics
– chapter 1, excluding special topics
topic 2: foundation for inference
– chapter 2
topic 3: comparing groups
– chapter 4.1-4.3
topic 4: linear regression part I
– chapter 2.1-2.4, 2.6.6 and 5.1-5.3
topic 5: linear regression part II
– chapter 5.4 and 6, excluding 6.4
topic 6: linear regression part III
– extra material
● topic 1: introduction to statistics
inter-ocular traumatic test, the measurements speak for itself so there is no need for statistics
statistics, learning and drawing conclusions from data under uncertainty
– frequentist statistics, concerned with how often we expect something to happen by chance
– bayesian statistics, concerned with how likely we think something is
observations, variables and data matrices
data matrices are a convenient way to record and store data
– each row in the table represents a case
– columns represent characteristics, called variables
– numerical variables
– continous variables, can take a wide range of numerical values
– discrete variables, can only take numerical values with jumps
– categorical variables
– regular categorical variables, characterized by the ability to only qualitatively classify or
categorize
– ordinal variables, characterized by the ability to categorize a variable and its relative position in
relation to other variables
, overview of data collection principles
the target population is every case of the group that is being studied
a sample represents a subset of the cases and is often a small fraction of the population
– it is essential to draw a representative sample, and avoid bias
– simple random sample, the most basic random sample is called a
– convenience sample, sample where individuals who are easily accessible are more likely to be included
if we suspect a certain variable affects another variable, that variable is called to explanatory variable; the
variable that we suspect to be affected by the explanatory variable is called the response variable
– however, association does not imply causation
there are two primary types of data collection
– observational studies, when data is collected by the researchers in a way that does not directly interfere
with how the data arise
– experiments, when researchers want to investigate the possibility of a causal connection
sampling biases
– non-response, occurs if only a small fraction of a randomly sampled people actually respond to the
survey
– convenience sampling, sample where individuals who are easily accessible are more likely to be
included
experiments
in experimental research, the participants are divided between a treatment group and a control group
randomization and replication reduce bias and uncertainty
– randomization is done to account for variables that cannot be controlled
– replication is done to accurately estimate the effect of the explanetory variable on the response; in a
single study, we replicate by collecting a sufficiently large sample
blinding, when researchers keep the patients uninformed about their treatment to prevent psychological
effects
examining numerical data
a scatterplot provides case-by-case view of data for two numerical variables
– a dot plot is a one-variable scatterplot; the mean is a common way to measure the center of a
distribution of data
a histogram is a figure where the datapoints are collected into “bins” and plotted as bars, they are convenient
for describing the shape of the data distribution
– right-skewed shape, when data trails of to the right with a long tail
– left-skewed shape, data with a long, thin tail to the left
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