The Nature of Probability and Statistics Chapter 1 Review The Nature of Probability and Statistics

Statistics Science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data Reasons for study: 1. Be able to read and understand statistical studies 2. Be able to conduct your own studies and research 3. Be able to use knowledge from studying statistics to make better decisions as consumers and citizens

Two Branches of Statistics Statistics can be divided into two separate branches, depending on how the data is used. Descriptive Statistics – the collection, organization, summarization, and presentation of data Inferential Statistics – generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions (uses probability)

Types of Data Variables (data) can be classified into two different types: Qualitative – can be placed into distinct categories, according to some characteristic or attribute (keyword is qualities) Quantitative – numerical and can be ranked (keyword is quantity, think “numbers”)

Measurement Scales Measurement scales are used to classify how variables are categorized, counted, or measured. There are four types: Nominal – classifies data into non-overlapping (mutually exclusive), exhausting categories where there is no order or ranking (example: gender, eye color, political affiliation) Ordinal – classifies data into categories that can be ranked (example: letter grades, rating scales, judging) Interval – ranks data, no true zero exists (example: SAT score, IQ test, temperature) Ratio – ranks data, true zero exists, true ratios exist when the same variable is measured on two different members of the population (examples: height, weight, time, age)

Data Collection & Sampling Many times, it is not possible to survey an entire population of subjects. Therefore, the following sampling techniques are used: Random Sampling – subjects are selected using chance methods or random numbers Systematic Sampling – subjects are selected using every kth after the first subject is random selected from 1 through k Stratified Sampling – population is divided into groups (strata), then subjects are randomly selected from each group Cluster Sampling – subjects are selected by using an already intact group that is representative of the population (geographic area)

Types of Statistical Studies Two types of studies exists: Observational Study – researcher merely observes what is happening, or what has already happened and draws conclusions based on theses observations (no researcher intervention) Experimental Study – researcher manipulates one of the variables and tries to determine how the manipulation influences other variables

Key words Variable – characteristic or attribute that can assume different values Data – value that variables can assume Data set – collection of data values Population – all subjects that are being studied Sample – group of subjects selected from the population (a subset) Discrete variables – assume values that can be counted Continuous variables – assume an infinite number of values between any two specific values (often obtained by measuring and consist of fractions and decimals

Key words cont. Quasi-experimental Study – used when random assignment of subjects is not possible and intact groups are used Independent variable – variable that is being manipulated Dependent variable – resultant or outcome variable Treatment group – group receiving the special instruction and/or manipulation Control group – group that is not manipulated Hawthorne effect – result of subjects changing their behavior because of knowledge that they are participating in a study Confounding variable – variable that influences the outcome but was not separated from the independent variable