MATH 203 Study Guide - Fall 2018, Comprehensive Midterm Notes - Variance, Standard Deviation, Lung Cancer
12 Oct 2018
School
Department
Course
Professor
MATH 203
MIDTERM EXAM
STUDY GUIDE
Fall 2018
Week 1
Lecture 1
What is statistics?
• Often presented on numerical description
• Efficiency rate / percentage
Statistical applications:
• Descriptive - is numerical and graphical representations of data
• Inferential (more important) - about a population using data from a sample
o Estimates
o Decisions
o Predictions
Population: set of people, machines, trees, animals, transactions that we want to study.
Sample: a subset of the population under study
*Population is always bigger than sample
Elements of a good statistical analysis:
• Objectives of the study; What questions do we want to answer?
• Experiment; people, transactions, machines, etc. Depends on what we want to study - The
"subjects"
• Population under study
• Characteristics of interest: variables measured on the experiment units
o Quantitative variables: numerical
o Qualitative variables: category
o There can be a mix of quantitative and qualitative
• Sample: a subset of the population under study
Data collection
• Once we know the objectives, population, experimental units, variables of interest, we
collect data
• Methods:
o Experimental studies
o Observational studies
o Use already published data
o Surveys
Experimental studies
• Researcher designs the experiment and has the control over the experimental units
o i.e. study the effect of a new treatment on a disease
Sometimes it's unethical or not possible to assign a treatment to a subject
• i.e. you can't conduct an experiment on lung cancer by telling people to smoke. You can
only observe what happened to someone that was already a smoker
find more resources at oneclass.com
find more resources at oneclass.com
Week 1
Experimental: control study
Observational: the researcher is not applying a change themselves
Lecture 2
Methods for summarizing data:
• Graphical
• Numerical
Both work for quantitative and qualitative
Incorporating a second variable allows for cross-classification
Simpson's Paradox: When a 3rd variable (confounding factor) changes the interpretation of the
relationship between 2 other variables
Methods for quantitative data:
• Centre of the data
o The sample mean/sample average is denoted by x=(x1+x2+…+xn)/n
• Spread
• Shape
• Weird things (outliers)
Sample median:
• Let x1, x2,…xn be a set of numbers. The median is denoted by m. It's the "middle" number
in the sense that if we ordered the set from smallest to largest, m would be in the middle.
• If n is odd, m is the number in the (n+1)/2'th position in the ordered list
• If n is even, we find the numbers in position (n/2) and (n/2)+1 in the ordered list. We then
calculate the average of those two numbers
• 50% of data points are below and above the median number
• Before getting the median, we need to order the data
Sample mode:
• The most frequently occurring observation
• If all data points occur exactly once, then every data point is a "mode"
Measures of spread: sample range and sample variance
• Sample range is denoted by R
Let x1, x2, xn be as set of numbers
Let xL = the largest value of those numbers
Let xs = the smallest value
R = xL - xs
• Sample variance is denoted by s2
S2 is the E(xi-xmean)2 /(n-1)
find more resources at oneclass.com
find more resources at oneclass.com
3
MATH 203 Full Course Notes
Verified Note
3 documents
Document Summary
What is statistics: often presented on numerical description, efficiency rate / percentage. Statistical applications: descriptive - is numerical and graphical representations of data. Inferential (more important) - about a population using data from a sample: estimates, decisions, predictions. Population: set of people, machines, trees, animals, transactions that we want to study. Sample: a subset of the population under study. Elements of a good statistical analysis: objectives of the study; what questions do we want to answer, experiment; people, transactions, machines, etc. Depends on what we want to study - the. "subjects: population under study, characteristics of interest: variables measured on the experiment units, quantitative variables: numerical, qualitative variables: category, there can be a mix of quantitative and qualitative, sample: a subset of the population under study. Data collection: once we know the objectives, population, experimental units, variables of interest, we collect data, methods, experimental studies, observational studies, use already published data, surveys.
