Stats chapter 1

Data

Collections of observations, such as measurements, genders, or survey responses;

Statistics

The science of planning studies, collecting, organizing, summarizing, presenting, analyzing, interpreting data, and drawing conclusions;

Population

The complete collection of all measurements or data being studied;

Census

Collection of data from every member of a population;

Sample

A subset of members selected from a population;

Voluntary Response Sample

A sample in which people choose themselves whether to participate; prone to bias;

Prepare

First step of the statistical process; understand the context, data source, and sampling method;

Analyze

Second step of the statistical process; graph, explore, and analyze data using appropriate methods;

Conclude

Third step of the statistical process; interpret results and draw conclusions;

Statistical Significance

Occurs when the likelihood of an event happening by chance is 5% or less;

Practical Significance

Determines whether a finding makes a meaningful real-world difference worth its cost or effort;

Misleading Conclusions

Pitfall involving unclear, confusing, or overly technical statements about data;

Sample Data Reported Instead of Measured

Pitfall in which subjects report results instead of researchers taking direct measurements;

Loaded Questions

Questions worded to influence or bias responses;

Nonresponse

Error or bias that occurs when selected individuals refuse or fail to participate;

Low Response Rate

When few selected individuals respond, potentially reducing reliability and increasing bias;

Misuse of Percentages

Pitfall involving incorrectly reported or unjustified percentages;

Parameter

A numerical measurement describing a characteristic of a population;

Statistic

A numerical measurement describing a characteristic of a sample;

Quantitative Data

Numerical data representing counts or measurements;

Discrete Data

Quantitative data with a finite or countable number of possible values;

Continuous Data

Quantitative data that can take infinitely many possible values within a range;

Categorical Data

Data consisting of names, labels, or attributes rather than numerical counts or measurements;

Nominal Level

Data consisting of categories with no meaningful order;

Ordinal Level

Data that can be ordered, but differences between values are meaningless or cannot be determined;

Interval Level

Data that can be ordered and have meaningful differences, but lack a natural zero;

Ratio Level

Data that can be ordered, have meaningful differences, and have a natural zero;

Big Data

Data sets so large or complex that traditional software tools are insufficient;

Data Science

A field combining statistics, computer science, software engineering, and other disciplines;

Missing Completely at Random

Missing data whose absence is independent of its value and other values;

Missing Not at Random

Missing data whose absence is related to the value itself or the reason it is missing;

Deleting Cases

A method of handling missing data by removing cases with missing values;

Imputation

A method of handling missing data by substituting replacement values;

Observational Study

A study that observes and measures individuals without attempting to change them;

Experiment

A study that applies a treatment and observes its effects;

Experimental Unit

An individual or object receiving a treatment in an experiment;

Subject

A person participating in an experiment;

Gold Standard

An experimental approach using randomization and placebo or treatment groups;

Placebo

A harmless, ineffective procedure or pill used for comparison;

Replication

Repeating an experiment on multiple individuals with a sufficiently large sample to observe treatment effects;

Blinding

Keeping subjects unaware of whether they receive the treatment or placebo;

Double-Blind Study

A study in which neither subjects nor experimenters know who receives the treatment or placebo;

Randomization

Using chance to assign subjects to groups, helping create comparable groups;

Simple Random Sample

A sample in which every possible sample of a given size has the same chance of selection;

Systematic Sampling

Selecting a starting point and then choosing every kth member of a population;

Convenience Sampling

Selecting individuals who are easiest to access;

Stratified Sampling

Dividing a population into distinct subgroups and sampling from each subgroup;

Cluster Sampling

Dividing a population into clusters, randomly selecting clusters, and including all members of selected clusters;

Multistage Sampling

Collecting data using a combination of sampling methods across multiple stages;

Cross-Sectional Study

An observational study collecting data at one point in time;

Retrospective Study

An observational study examining past data through records or interviews;

Case-Control Study

A retrospective study that compares groups based on an outcome or condition;

Prospective Study

An observational study collecting data in the future from groups sharing common factors;

Longitudinal Study

A study that collects data over time;

Cohort

A group of individuals sharing common characteristics or factors in a study;

Confounding

When the effects of multiple factors cannot be separated, making the specific cause unclear;

Completely Randomized Experimental Design

An experimental design that assigns subjects to treatment groups entirely by chance;

Randomized Block Design

An experimental design that divides subjects into similar blocks and randomly assigns treatments within each block;

Matched Pairs Design

An experimental design comparing paired subjects or two related measurements;

Rigorously Controlled Design

A design that carefully makes treatment groups similar in important ways;

Sampling Error

The difference between a sample result and the true population result caused by chance variation;

Nonsampling Error

Error caused by factors such as incorrect data entry, calculation mistakes, biased questions, or false responses;

Nonrandom Sampling Error

Error or bias resulting from nonrandom sampling methods such as convenience or voluntary response sampling;

Statistical Thinking

Using critical thinking, common sense, and context to interpret statistical results;

Why is data type important?

It helps determine which statistical methods are appropriate for analyzing the data;

What is the difference between a population and a sample?

A population includes the entire group being studied; a sample is a subset of that group;

What is the difference between a parameter and a statistic?

A parameter describes a population; a statistic describes a sample;

What is the difference between discrete and continuous data?

Discrete data are countable; continuous data can take infinitely many values within a range;

What is the difference between categorical and quantitative data?

Categorical data represent labels or groups; quantitative data represent numerical counts or measurements;

Which measurement level has no order?

Nominal;

Which measurement level has order but meaningless differences?

Ordinal;

Which measurement level has meaningful differences but no natural zero?

Interval;

Which measurement level has a natural zero?

Ratio;

What are the three steps of a statistical study?

Prepare, Analyze, Conclude;

What is the main problem with voluntary response samples?

They are prone to bias because participants choose whether to respond;

What is the difference between an observational study and an experiment?

An observational study measures without intervention; an experiment applies a treatment;

What is the difference between single-blind and double-blind studies?

In a single-blind study, subjects do not know their treatment; in a double-blind study, neither subjects nor experimenters know;

What is the purpose of randomization?

To reduce bias and help create comparable groups;

What is the purpose of replication?

To observe treatment effects across enough subjects and reduce the influence of chance variation;

What is the difference between stratified and cluster sampling?

Stratified sampling selects members from every subgroup; cluster sampling selects certain groups and includes all their members;

What is the difference between systematic and simple random sampling?

Systematic sampling selects every kth member after a starting point; simple random sampling gives every possible sample of a given size an equal chance;

What is the difference between sampling and nonsampling error?

Sampling error comes from chance variation; nonsampling error comes from other problems such as mistakes or bias;

What is the difference between statistical and practical significance?

Statistical significance concerns the likelihood of chance results; practical significance concerns real-world importance;

What does confounding make difficult?

Identifying which factor caused an observed effect;

What is a placebo effect?

A response caused by expectations or beliefs rather than the active treatment;

What is the difference between retrospective and prospective studies?

Retrospective studies examine the past; prospective studies collect data going forward;

What is the purpose of blocking in an experiment?

To group similar subjects together before randomly assigning treatments;

What is a matched pairs design useful for?

Comparing two related measurements or closely matched subjects;

How can missing data be handled?

Delete cases with missing values or impute replacement values;

What is the difference between missing completely at random and missing not at random?

Completely at random means missingness is independent of the data; not