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Introductory Statistics: Basic Definitions and Key Concepts - Prof. Samuel P. Wilcock, Study notes of Statistics

Messiah CollegeStatistics
Prof. Samuel P. Wilcock

An overview of basic definitions and key concepts in introductory statistics, including data, statistics, populations, samples, parameters, and statistics. It also covers the branches of statistics, ways to classify data, and the general method of statistical inquiry. The document also introduces various types of studies, sampling methods, and errors involved in collecting data.

Typology: Study notes

Pre 2010

Uploaded on 08/19/2009

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NAME
STAT 269 - Introductory Statistics
Basic Denitions
Data
: pieces of information to which meaning has been attached
Statistics
: a collection of methods for planning experiments, obtaining data, and then organizing,
summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.
Basic Terms
{ Population
: the complete set of all individuals or units that are of interest in the study
{ Sample
: the subset of the population that is actually studied
Two Key Types of Numbers
{ Parameter
: a numerical measurement, usually unknown, describing some characteristic of a
population
{ Statistic
: a numerical measurement describing some characteristic of a sample
Branches of statistics
{ Experimental Design
: the branch of statistics that deals with planning experiments and ob-
taining data
{ Descriptive Statistics
: the branch of statistics that deals with organizing, summarizing and
presenting data
{ Inferential Statistics
: the branch of statistics that deals with analyzing, interpreting, and
drawing conclusions based on the data
Three ways to classify data
{ Quantitative vs. Qualitative
Quantitative Data
: data that represents counts or measurements, answers the questions
\how much?" or \how many?", usually numerical
Qualitative Data
: data that separates units into categories by some non-numeric charac-
teristic
{ Discrete vs. Continuous
Discrete Data
: any type of data where the possible values can be listed out completely
Continuous Data
: data where the possible values fall along an interval, and any list would
miss many possible values
{ Levels of Measurement
Nominal Level
: names, labels, or categories that cannot be sorted
Ordinal Level
: data values can be arranged, but dierences between values are meaningless,
if they even exist
Interval Level
: dierences make sense, but there is no natural zero, that is, the value 0 does
not correspond to nothing
Ratio Level
: there is a natural zero so dierences and ratios make sense
pf2

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NAME

STAT 269 - Introductory Statistics

Basic De nitions

 Data: pieces of information to which meaning has been attached

 Statistics: a collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

 Basic Terms

{ Population: the complete set of all individuals or units that are of interest in the study { Sample: the subset of the population that is actually studied

 Two Key Types of Numbers

{ Parameter: a numerical measurement, usually unknown, describing some characteristic of a population { Statistic: a numerical measurement describing some characteristic of a sample

 Branches of statistics

{ Experimental Design: the branch of statistics that deals with planning experiments and ob- taining data { Descriptive Statistics: the branch of statistics that deals with organizing, summarizing and presenting data { Inferential Statistics: the branch of statistics that deals with analyzing, interpreting, and drawing conclusions based on the data

 Three ways to classify data

{ Quantitative vs. Qualitative  Quantitative Data: data that represents counts or measurements, answers the questions \how much?" or \how many?", usually numerical  Qualitative Data: data that separates units into categories by some non-numeric charac- teristic { Discrete vs. Continuous  Discrete Data: any type of data where the possible values can be listed out completely  Continuous Data: data where the possible values fall along an interval, and any list would miss many possible values { Levels of Measurement  Nominal Level: names, labels, or categories that cannot be sorted  Ordinal Level: data values can be arranged, but di erences between values are meaningless, if they even exist  Interval Level: di erences make sense, but there is no natural zero, that is, the value 0 does not correspond to nothing  Ratio Level: there is a natural zero so di erences and ratios make sense

 General Method of Statistical Inquiry

  1. Form a speci c question to be answered
  2. Collect data according to some design (randomness)
  3. Analyze data and form conclusions

 Types of Studies

{ Census: a study of all the units in the population { Observational Study: a study where results are simply observed and measured, there is no control { Experiment: a study where some treatment is applied and the e ect is observed, often can be ethically problematic  Completely Randomized Design (CRD): each subject is assigned to a treatment group completely at random without regard to any other factors  Confounding: this is what happens if the e ect of two factors cannot be distinguished from each other  Blocking: putting subjects randomly into di erent groups according to some important factor, so that each level of the treatment is represented fairly across the levels of the blocking factor  Placebo: a way of studying the psychological e ects of a treatment, looks, tastes, feels, etc. just like the real treatment  Blinding: not letting the subject know whether they are in a treatment or placebo group, in medical studies the patient's doctor also is not informed of which group the patient is in so that they cannot hint at the truth (this is called a double blind experiment) { Simulation: using a model of the situation, use the computer to generate data

 A Biased Sample: a sample in which the units selected or the data gathered are not representative of the population as a whole

 Sampling Methods

{ Random Sample: each subject has the same chance of being selected { Simple Random Sample (SRS): each sample of size n is equally likely { Systematic Sampling: take every kth subject after some random starting point { Strati ed Sampling: subdivide the population into several large subgroups (or strata) and conduct a SRS within each { Cluster Sampling: subdivide the population into many small clusters, then randomly select some of the clusters and use all of the subjects within each selected cluster { Convenience Sampling: use whichever subjects are easiest to get

 Two Types of Errors Involved with Collecting Data

{ Sampling Error: the di erence between a sample result and the true population that is due entirely to random variations { Nonsampling Error: refers to all variations that are not due to random chance such as non- random samples, misrecorded data, subjects lying on surveys, poorly worded questions, etc.