Chapter 1: Introduction to Statistics

Population

a group of interest

Sample

subset of a population

Variable

a value that can change among the numbers of a population

Data

the count/measurement/observation of some variable in a population/sample

• Used to get information on/make statements about a population

Census

a study in which data are collected from every member of a population

Parameter

a numerical description of a population’s characteristics

Sample Statistics

numerical descriptions of a sample’s characteristics

Statistics

the science of gathering, describing, and analyzing data

Descriptive Statistics

gathers, sorts, summarizes, and displays the data

Inferential Statistics

uses descriptive statistics to estimate population parameters

Quantitative Data

numerical count or measurement

Ex:

• amount of red dye needed

• the number of colors available

Continuous Data

can take on any value in a given range & are usually measurements

Ex:

• temperature

• heights

Discrete Data

can only take on particular values & are usually counts

Ex:

• # of houses in a neighborhood

• # of machines at the gym

Qualitative Data

labels or descriptions of traits (categorical data)

Ex:

• shades of paint

• rankings of popular colors

nominal levels

labels or names (a.k.a. categories)

Ex:

• colors

• car models

ordinal levels

Labels can be arranged in a meaningful order, but calculations (like adding or dividing) don’t make sense

Ex:

• rankings

interval levels

can also be arranged in a meaningful order, & the differences between data entries are meaningful

Ex:

• grouped ages (18-49, 50-70)

ratio levels

can be ordered, differences are meaningful, & the zero point means the absence of something

Ex:

• grouped temperatures

The Process of a Statistical Study

1. Determine the Design of the Study

   1. State the questions to be studied

   2. determine the population and variables

   3. Determine the Sampling Method

2. Collect the data

3. Organize the data

4. Analyze the data to answer the question

Observational Study

observe data that already exist

Cross-sectional Study

data are collected @ a single point in time

Longitudinal Study

data are gathered over a period of time

Meta-Analysis

a study that compiles information from previous studies

Case Study

looks @ multiple variables that affect a single event

Experimental Study

generate data to help identify cause-and-effect relationships

Principles of Experimental Design

1. Randomize the control and treatment groups

2. Control outside effects on the response variable

3. Replicate the experiment a significant # of times to see meaningful patterns

treatment

describes some condition that is applied to a group of subjects in an experiment

subject

a person or thing being studied in an experiment

participant

what the subject is if they’re human

explanatory variable

The variable that causes a change in the response variable (independent variable) (cause)

response variable

the variable that responds to the treatment (dependent variable) (effect)

control group

group of subjects to which no treatment is applied

treatment group

the group of subjects to which treatment is applied

confounding variables

factors other than the treatment that cause an effect (or alteration) in the subjects

the placebo effect

a response to the power of suggestion (or lies), rather than the treatment itself, by the participant

placebo

a substance that appears identical to the actual treatment, but has no beneficial elements

single-blind

subjects don’t know whether they’re in the control or treatment group, but researchers do

double-blind

neither the subjects nor the researchers know which groups (control, treatment, or placebo) the subjects are in

representative sample

has the same relevant characteristics as the population and does not favor one group or another

Random Sample

every member has an equal chance of being selected

Simple Random Sample

every sample (out of the population) has an equal chance of being selected

Stratified Sample

the population is divided into sub-groups (called “strata”) and the same # of subjects are chosen from each strata/sub-group

Cluster Sample

the population is divided in to sub-groups (called “clusters”) that are similar to the whole population, and whole clusters are chosen at random

Systematic Sample

selecting every nth member of the population

Ex:

• selecting every 3rd bottle

Convenience Sample

the sample is convenient for the researcher to select