Stats - Block 1

Statistics

The study of procedures for collecting, describing, and drawing conclusions from information

Statistics involves…(4)

• Formulating questions.

• Collecting data needed to answer the questions

• Describing the data

• Drawing conclusions, using appropriate methods

Population

The entire collection of individuals

Sample

A subset of a population containing the individuals that are observed

Subset

A set of elements that are part of/taken from a larger set

The best sampling methods all involve…

Random Selection

The most basic sampling method is

Simple Random Sampling

Simple Random Sampling

A sample chosen in which each collection of however many population items is equally likely to make up the sample

Population (Item)

The entire set of items or individuals that share a common characteristic and are of interest to the study

Sample of Convenience

Sample selected without following a well-defined random process

When is a sample considered a sample of convenience?

When the sample itself differs systematically from the population; otherwise it’s a simple random sample

Stratified Sampling

The population is divided into groups (strata) and a simple random sample is drawn from each group (stratum)

Cluster Sampling

Items are randomly selected in groups, or clusters, from the overall population.

• Useful when the population is too large and spread out for simple random sampling to be feasible

Systematic Sampling

Items are ordered, and every kth item is selected for the sample

• Often used to sample products on an assembly line to ensure they meet quality standards

Voluntary Response Sampling

Calls for volunteers to participate in an experiment; NEVER RELIABLE due to bias

Why is Voluntary Response Sampling unreliable?

• People who volunteer an opinion tend to have stronger opinions than is typical of the population.

• People with negative opinions are often more likely to volunteer their response

Pararmeter

A number that describes a population (ex. avg clasas exam score)

Statistic

A number that describes a sample (ex. sample of 6 female students avg score)

Experimental Units

The individuals studied

Outcome

What is measured/recorded

Treatment

Procedurees applied to each experimental unit

Randomized Experiment

The investigator assigns treatments to the experimental units at random

Observational Study

The assignment of treatments is not made by the investigator

Placebo Effect

The improvement in condition simply from believing they’re receiving treatment.

Double-Blind Experiment

Neither the investigators nor the subjects know who has been assigned to which treatment

Randomized Block Experiments

Subjects are divided into homogenous blocks

Matched Pairs Experiment

Each block consists of two subjects selected to be as similar as possible and are randomly assigned to different treatments (typically age or sex)

• ex. In a study of a new weight-loss drug, pairs of subjects are matched by age, sex, and weight. One member of each pair receives the drug, while the other receives a placebo

Cohort Study

A group of subjects is studied to determine whether various factors of interest are associated with an outcome

Prospective Cohort Study

The subjects are followed over time

Cross Sectional Cohort Study

Measurements are taken at one point in time

Retrospective/Case Controlled Study

Subjects are sampled after the outcome has occurred

Descriptive Statistics

Organizing and summarizing data

Inferential Statistics

Extends the results of a sample to draw conclusions about a population (ex. getting a voter approval rate of 42% and adding/subtracting the 3% margin of error to your to your findings)

Process of Statistics

1. Determine the research objective

2. Collect data

3. Describe the data

4. Make appropriate inference(s)

Discrete Variable

Quantitative variable with a finite/countable number of possible values

Continuous Variable

Quantitative variable with a finite/countable number of possible values

Nominal

Values of the variable name, label, or categorize

Ordinal

Nominal + can be ranked from higher to lower

Interval

Ordinal + subtraction makes since, zero has meanng (ex. 00:00 military time, zip codes)

Ratio

Interval + zero has meaning, ratios do (ex. $0)

Sampling Frame

List of the members in a population being studied at fixed points in time

Multi-stage sampling

Select individuals from a strata and then select some individuals

Sampling Bias

Bias is in the sampling technique

Nonresponse Bias

Those that don’t respond to the survey have different opinions from those that do

Response Bias

True opinions aren’t reflected in the survey

Non-sampling Errors

When bias causes error

Sampling Error

A sample gives incomplete info about a population

Qualitative Data

Words/Categories/Labels

Quantitative Data

Numerical

Frequency

The number f times it occurs in the data set

Relative Frequency

The proportion of observations in a category/Sum of all frequencies

____ visually represent a frequency distribution

Bar Graphs

Pareto Chart