Stats unit 4 vocab

Population

In a statistical study, the entire group of individuals we want information about.

Census

Collects data from every individual in the population. 

Sample

Subset (smaller group) chosen from the population to collect data from

Why Do We Use a Sample? 

1. It can be easier to collect data from a smaller group of people 

2. If the sample is representative of the population, it can be used to make inferences about the population.

Sample Survey

a study that collects data from a sample that is chosen to represent a specific population

3 Steps for Planning a Sample Survey

1. Identify the population of interest in the study

2. Decide what we would like to measure (response variable)

3. Decide how to choose the sample from the population (see “good sampling methods” for options)

Good Sampling Methods

1. Simple Random Sample

2. Stratified Sample

3. Cluster Sample

4. Systematic Sample

Bad Sampling Methods

1. Convenience Sampling - when members of a population are not chosen at random, but are chosen because they are easy to access

2. Voluntary Response Sampling - allows people to choose to be in the sample by responding to a general invitation (think internet polls, Yelp reviews, call-in/write in responses)

Bias

When design flaws in a study lead to likely overestimates or underestimates of the value we want to know.  

***This is not just bad luck in one sample, but a design flaw that would continue to cause problems, even if another sample was taken. 

When Asked to Describe Bias, You Must Do 2 Things

1. describe how members of the sample might respond differently from the rest of the population

2. explain how this difference would lead to an underestimate or overestimate

Random Sampling

using a chance process to determine which members of a population are included in the sample.

Simple Random Sample

A type of random sampling where every sample of size n has an equal chance to be selected.  

Commonly obtained through identical pieces of paper, a random number generator, or Table D

How to Take a Simple Random Sample with Technology

Label: Give each member of the population a number between 1 and N (where N is the population size)

Randomize: Use Math→PROB→RandInt
(lower: 1, upper: N, n: sample size)

Select: Choose individuals that correspond to the randomly selected individual

How to Take a Simple Random Sample with Table D

Label: Give each member of the population a distinct numerical label with the same number of digits. 

Randomize: Read consecutive groups of digits of the appropriate length from left to right across a line in Table D. Ignore any group of digits that wasn’t used as a label or that duplicates a label already in the sample. Stop when you have chosen n different labels.

Select: Choose the individuals that correspond to the randomly selected integers.

Strata

Groups of individuals in a population who share characteristics thought to be associated with the variables being measured in a study.

Stratified Sampling

Selects a sample by choosing a Simple Random Sample from each strata and combining the samples into one overall sample. 

Randomly select a few experimental units from each strata to create the sample.

Cluster

A group of individuals in the population that are located near each other.  Ideally, each cluster would be roughly representative of the population. 

Cluster Sampling

Selects a sample by randomly choosing clusters and including each member of the selected clusters in the sample.

Undercoverage

when some members of the population are less likely to be chosen or cannot be chosen in a sample.

Nonresponse

when an individual chosen for the sample can’t be contacted or refuses to participate.

Response Bias

when there is a systematic pattern of inaccurate answers to a survey question.  (can be due to a poorly written survey question or underlying bias introduced by environment or experimenter)

Observational Study

observes individuals and measures variables of interest but does not attempt to influence the responses.

Response Variable

measures an outcome of a study.

Explanatory Variable

may help explain or predict changes in a response variable.

Confounding

when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.

Experiment

deliberately imposes some treatment on individuals to measure their responses.

Placebo

a treatment that has no active ingredient, but is otherwise like other treatments.

Treatment

a specific condition applied to the individuals in an experiment (could be an active treatment or inactive treatment)

Experimental Units

the object to which a treatment is randomly assigned.  These are the participants in an experiment.

Subjects

When the experimental units are human beings

Factor

a variable that is manipulated and may cause a change in the response variable in an experiment.

Level

The different values of a factor

Fundamental Counting Principle

Describes the number of different combinations of factors and levels to describe the total number of outcomes (often displayed in a tree diagram).  Multiply the number of factors by the number of levels in each factor.

4 Key Features of Experimental Design

1. Comparison 

2. Random Assignment 

3. Control 

4. Replication

Control Group

used to provide a baseline for comparing the effects of other treatments.

Control

When other variables are kept constant for all experimental units (regardless of treatment group) to minimize the effects of confounding.

Placebo (2)

An inactive treatment used as part of the control group.  It looks, smells, and tastes like the treatment, but lacks the active ingredient being tested.

Placebo Effect

some subjects in an experiment will respond favorably to any treatment, even an inactive treatment.

Double-Blind

neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.

Single-Blind

either the subjects don’t know which treatment they are receiving or the people who interact with them and measure the response variable don’t know which subjects are receiving which treatment.

(usually it's the subject that doesn’t know which treatment they received - not the experimenter)

Random Assignment

Experimental units are assigned to treatments using a chance process.

It could be completely random design, randomized block design, or matched pairs design.

Completely Randomized Design

Divide the sample into “t” number of treatment groups.  Create a simple random sample of size n/t for treatment A, n/t for treatment B, and so on until all members of the sample are part of a group.

Randomized Block Design

Break the sample up into groups based on some characteristic that is thought to affect the response.  Break each block into “t” number of groups and assign each group to a treatment.

Block

a group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.

Matched Pairs Design

a common experimental design for comparing two treatments that uses blocks of size 2. In some matched pairs designs, two very similar experimental units are paired and the two treatments are randomly assigned within each pair. In others, each experimental unit receives both treatments in a random order.

Replication

using enough experimental units to distinguish a difference in the effects of the treatments from chance variation due to the random assignment.

Explain the Key Differences between Strata & Clusters

Strata and Clusters describe ways of breaking up the POPULATION into groups.  In strata, the POPULATION is broken up into groups based on similar characteristics.  In clusters, the POPULATION is broken up into groups by proximity but each cluster should be somewhat representative of the the population.

Explain the Key Differences between
Blocks & Matched Pairs

Blocks & Matched Pairs are ways of breaking up a SAMPLE into groups.  Blocks are where members of a SAMPLE are broken into groups based on similar characteristics.  Matched Pairs are where members of the SAMPLE are paired up with a similar member (or themselves) and then data is compared between the two.

Sampling Variability

different random samples of the same size from the same population produce different estimates.  We expect there to be some variability between samples due to inherent differences between people/items.

Sampling Variability & Sample Size

We expect larger samples to produce estimates that are closer to the true population parameters

Statistical Significance (Statistically Significant)

When the observed results of a study are too unusual to be explained by chance alone

The Scope of Inference:  When can we apply inferences to a population?

When the sample is selected randomly (using a simple random sample, appropriate stratified sample, or appropriate cluster sample)

The Scope of Inference: When can we make inferences about cause and effect?

When there is random assignment between treatment groups (appropriate use of randomized design, matched pairs design, or randomized block design)

Basics of Data Ethics

• All planned studies must be reviewed in advance by an institutional review board charged with protecting the safety and well-being of the subjects.

• All individuals who are subjects in a study must give their informed consent before data are collected.

• All individual data must be kept confidential. Only statistical summaries for groups of subjects may be made public.