Module 1: Descriptive Statistics

Data

Consist of information from observations, counts, measurements, or responses.

Statistics

The science of collecting, organizing, analyzing, and interpreting data in order to make decisions.

Parameter

A number that describes a population characteristic.

Ex: Average age of all people in the United States

Statistic

A number that describes a sample characteristic.

Example:  Average age of people from a sample of three states

Descriptive Statistics

involves organizing, summarizing, and displaying data.

Example: Tables, charts, averages  

Inferential Statistics 

Involves using sample data to draw conclusions about a population.

Qualitative Data 

Consists of attributes, labels, or non-numerical entries.

Quantitative Data 

Numerical measurements or counts.

Discrete data

Only certain numbers are possible data values (typically the result of a counting process).

Continuous data

Results when there are no gaps, interruptions, or jumps between possible data values within the range of values (typically the result of a measurement process).

Observational study 

A researcher observes and measures characteristics of interest of part of a population.

Example: Researchers observed and recorded the mouthing behavior on nonfood objects of children up to three years old. (Source: Pediatric Magazine)

Experiment

A treatment is applied to part of a population and responses are observed.

Example: An experiment was performed in which diabetics took cinnamon extract daily while a control group took none. After 40 days, the diabetics who had the cinnamon reduced their risk of heart disease while the control group experienced no change. (Source: Diabetes Care)

Simulation

A researcher uses a mathematical or physical model to reproduce the conditions of a situation or process.

Often involves the use of computers.

Example: Automobile manufacturers use simulations with dummies to study the effects of crashes on humans.

Confounding variables

occur when an experimenter cannot tell the difference between the effects of different factors on a variable.

Example: A coffee shop owner remodels her shop at the same time a nearby mall has its grand opening. If business at the coffee shop increases, it cannot be determined whether it is because of the remodeling or the new mall.

Key Elements of Experimental Design: Control

Placebo effect

a subject reacts favorably to a placebo when in fact he or she has been given no medical treatment at all.

Blinding 

is a technique where the subject does not know whether he or she is receiving a treatmentor a placebo.

Double-blind 

experiment neither the subject nor the experimenter knows if the subject is receiving a treatment or a placebo.

Randomization 

is a process of randomly assigning subjects to different treatment groups.

Completely randomized design 

subjects are assigned to different treatment groups through random selection.

Randomized block design

divide subjects with similar characteristics into blocks, and then within each block, randomly assign subjects to treatment groups.

Example: An experimenter testing the effects of a new weight loss drink may first divide the subjects into age categories. Then within each age group, randomly assign subjects to either the treatment group or control group.

Matched Pairs Design

subjects are paired up according to a similarity. One subject in the pair is randomly selected to receive one treatment while the other subject receives a different treatment.

Replication 

Is the repetition of an experiment using a large group of subjects.

Example: To test a vaccine against a strain of influenza, 10,000 people are given the vaccine and another 10,000 people are given a placebo. Because of the sample size, the effectiveness of the vaccine would most likely be observed.

Simple Random Sample 

Every possible sample of the same size has the same chance of being selected.

A Simple Random Sample can be created as follows:

Random numbers can be generated by a random number table, a software program or a calculator.

Assign a number to each member of the population.

Members of the population that correspond to these numbers become members of the sample.

Example: There are 731 students currently enrolled in statistics at your school. You wish to form a simple random sample of eight students to answer some survey questions.  Assign a number to each student.  Generate 8 random numbers between 1 and 731 using a random number table or technology.  Survey the students with the corresponding numbers.

Stratified Sample

Divide a population into groups (strata) and select a random sample from each group. 

Example: To collect a stratified sample of the number of people who live in West Ridge County households, you could divide the households into socioeconomic levels and then randomly select households from each level.

Cluster Sample

Divide the population into groups (clusters) and select all of the members in one or more, but not all, of the clusters. 

Example: In the West Ridge County example you could divide the households into clusters according to zip codes, then select all the households in one or more, but not all, zip codes.

Systematic Sample

Choose a starting value at random. Then choose every kth member of the population. 

Example: In the West Ridge County example you could assign a different number to each household, randomly choose a starting number, then select every 100th household.

Convenience Sampling 

Use results that are easy to get

Example: Stand on a street corner in West Ridge County and collect data from anyone who is willing to talk to you.

Ratio

Quantitive data measured on a scale with a true zero point

Nominal

Simplest level of measurement, classifies variables into distinct, mutually exclusive, and unlabeled categories or names that have no rank, order, or numerical value.

Ordinal

the value has a natural, meaningful rank or order. The exact distance or numerical difference between the categories is unknown, unequal, or cannot be measured.

Interval

Range of values used to estimate a population parameter, or a level of measurement where data has equal, ordered spaces between numbers but no true zero point

Class Width

The difference between two consecutive lower class limits or two consecutive upper class limits

Histogram

A visual tool used to represent and analyze data. Basically a graphic version of a frequency distribution, and can show the center, variation, and the shape of the distribution of the data.

Bell shape

When graphed it is seen as a “normal distribution”. The frequencies increase to a maximum, and then decrease, and symmetry, with the left half of the graph roughly a mirror image of the right half.