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Frequent Statistics Summary - Introductory Statistics with Randomization and Simulation (SOW-BKI138)

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Course
SOW-BKI138 (SOWBKI138)

Institution
Radboud Universiteit Nijmegen (RU)

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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Uploaded on September 23, 2024
Number of pages 15
Written in 2023/2024
Type Summary

david m diez
simulation
frequent statistics
artificial intelligence
bachelor
statistics
mean
openintro
foundation for inference
data
linear regression
num
introductory statistics with randomization
ai

Institution
Radboud Universiteit Nijmegen (RU)
Education
Artificial Intelligence
Course
SOW-BKI138 (SOWBKI138)

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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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