STS 132 Chapter 1

Statistics

is the process of collecting, organizing, summarizing,and analyzing data to draw conclusions or answer questions

Statistical conclusions

come with a measure of confidence (i.e., we will quantify how confident we are in our conclusions, like a margin of error)

Population

the entire group of individuals to be studied (Ex. students at UMaine)

Sample

a subset of the population (Ex. students at Umaine --> 20 students enrolled in STS 132 selected at random)

Individual

a member of the population (i.e. any student at UMaine)

A statistic

is a numerical summary of a sample

A parameter

is a numerical summary of a population

Descriptive statistics

involves organizing and summarizing the data obtained from a sample

Inferential statistics

involves taking a result about a sample, extending it to the whole population, then measuring the reliability of that result

The process of statistics

(1) Identify the research objective, (2) collect the data needed to answer the question, (3) describe the data, (4) perform inference

variables

are the characteristics of individuals in a population (note: these vary within individuals and among individuals)

Qualitative variable (categorical variable)

classify individuals based on some attribute or characteristic

Quantitative variables

provide a numerical measure of individuals (when in doubt these values can be added or subtracted to obtain meaningful results)

Discrete quantitative variable

its value results from counting

Continuous quantitative variable

its value is measured

Data

the set of observed values for a variable

Explanatory variable

In research, we determine how variation in this affects the value of the response variable

Response variable

In research, we determine how variation in the explanatory variable affects this

Observational study

measures the response variable without attempting to influence the value of the explanatory variable

Designed experiment

the researcher assigns individuals to groups, intentionally influences the value of the explanatory variable, and measures the value of the response variable for each group

Confounding

occurs when the effects of two or more explanatory variables are not separated. So any perceived relation between an explanatory variable and the response variable may be due to some other variable that was not accounted for

Lurking variable

An explanatory variable that was not considered in a study, but affects the value of the response variable (we manage these by considering whether the individuals in our study differ in any significant way

Observational studies allow

researchers to claim association but not causation

Benefits of observational studies

lower cost, better access to individuals, maybe more ethical

Confounding variable

an explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study

Categories of observational studies

cross-sectional, case-control, cohort

Cross-sectional studies

observational studies that collect info about individuals at a specific point in time, or over a very short period of time

case-control studies

These studies are retrospective, meaning they require individuals to look back in time or require the researcher to look at historical records

Cohort studies

Identifies a group of individuals to participate in the study. The group is then observed over a long period of time and characteristics about the individuals are recorded. These are prospective

Random sampling

the process of using chance to select individuals from a population to be included in the sample (chance = randomness)

Randomness

__________ is the key to obtaining a sample that's representative of the population

Convenience

Avoid using ________ to select a sample

Simple random sampling process

Identify the population (with N individuals), select a sample (of n individuals) in such a way that each individual has an equal chance of being selected

Frame

a list of all the individuals within the population

Sample without replacement

an individual who is selected is removed from the population and cannot be chosen again

Sample with replacement

a selected individual is placed back into the population and could be chosen a second time

Stratified sample

Is obtained by separating the population into non-overlapping groups called strata and then obtaining a simple random sample from each stratum (the individuals within each stratum should be homogeneous in some way)

Systematic sample

is obtained by selecting every kth individual from the population. The first individual selected is a random number between 1 and k

Steps in Systematic Sampling

N/n and round down to the nearest interval. This is k. Randomly select a number between 1 and k (p). The sample is p, p+k, p+2k..., p + (n-1)k

Cluster sample

is obtained by selecting all individuals within a randomly selected cluster or group of individuals

Convenience sample

the individuals are easily obtained and not based on randomness (we should be skeptical of these)

Voluntary response samples

Individuals in the sample are self-selected (meaning the individuals themselves decide to participate in the study). This is a type of convenience sample

Bias

A sample has this if it's not representative of the population

Three sources of bias

sampling bias, nonresponse bias, response bias

Sampling bias

occurs when the sampling methods tend to favor one part of the population over another

Undercoverage (source of sampling bias)

occurs when the proportion of one segment of the population is lower in a sample than it is in the population

Nonresponse bias

occurs when sampled individuals who do not participate in a survey have different opinions from those who do (can be improved through the use of callbacks or rewards/incentives)

Response bias

exists when the answers on a survey do not reflect the true feelings of the respondent

Types of response bias

Interviewer error, misrepresented answers, wording of questions, ordering of questions or words, type of question

Interviewer Error

Can be avoided with a trained/skilled interviewer

misrepresented answers

can cause response bias. some questions elicit inaccurate responses (Questions about salaries, crime)

Wording of questions

can cause response bias, but can be avoided by asking questions in a balance form and in a not vague way

Ordering of Questions or words

Can cause response bias, but can be avoided by distributing surveys with questions switched around

Open question

allows the respondent to write their own response (using their own words)

Closed question

requires the respondent to choose from a list of predetermined responses

Weakness of closed questions

Respondents are likely to choose earlier choices rather than later choices. Choices can be shuffled/rotated to mitigate this

Common practice regarding open/closed questions

conduct a small survey with open questions, then use common responses as choices for closed questions

Data entry error

Researcher enters the data wrong and that can lead to results that are not representative o the population

Sampling error

results from using a sample to estimate information about a population. This type of error is unavoidable because a sample gives incomplete information about a population

Nonsampling error

results from undercoverage, nonresponse bias, response bias, or data-entry error. Could be present even if we sampled the whole population.

experiment

is a controlled study conducted to determine the effect of one or more explanatory variables (aka factors) on a response variable

factors

explanatory variables

Treatment

Any combination of the values of the factors

Experimental unit (subject)

is a person, object, or some other well-defined item upon which a treatment is applied

control group

serves as a baseline treatment that can be used to compare to other treatments

Placebo

Inert medication, such as a sugar tablet or saline injection, that looks/tastes/smells like the experimental drug but has no effect otherwise

Blinding

refers to nondisclosure of the treatment an experimental unit is receiving

Single-blind experiment

the experimental unit (or subject) does not know which treatment they're receiving

double-blind experiment

neither the experimental unit nor the researcher in contact with the experimental unit knows which treatment the experimental unit is receiving

Design an experiment

means to describe the overall plan in conducting the experiment

Steps to designing an experiment

(1) Identify the problem to be solved, (2) determine the factors that affect the response variable, (3) determine the number of experimental units, (4) determine the level of each factor, (5) Conduct the experiment with replication, (6) test the claim

Claim

statement of the problem (should be explicit and must identify the response variable and the population to be studied)

Two ways to deal with factors

Control or randomize

set the level of a factor at one value throughout the experiment if...

you are not interested in its effect on the response variable

Set the level of a factor at various levels if...

you are interested in its effect on the response variable

Randomize a factor by...

randomly assigning the experimental units to treatment groups

Replication

when each treatment is applied to more than one experiment unit (should always be done)

inferential statistics

the process that allows us to make a conclusion about a population using results obtained from a sample

Completely randomized design

is an experimental design where each experiment unit is randomly assigned to a treatment

Matched-pairs design

an experimental design in which the experimental units are paired up (the pairs are matched up so that they are somehow related -- same person before and after, twins, same geographical location, husband/wife, etc.)

Blocking

the process of grouping together homogenous experimental units and then randomly assigning the experimental units within each group to a treatment

block

a group of homogenous individuals

Randomized block design

used when the experimental units are divided into homogenous groups called blocks. Within each, the experimental units are randomly assigned to treatments.

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