The Role of Statistics in Critical Thinking

A representative sample exhibits characteristics typical of those possessed by the target population. (Репрезентативная выборка показывает типичные особенности присущие изучаемой совокупности)

Collecting Data (Sources of Data)

Quantitative data are measurements that are recorded on a naturally occurring numerical scale.

Types of Data

A measure of reliability is a statement (usually quantified) about the degree of uncertainty associated with a statistical inference.

A statistical inference is an estimate, prediction, or some other generalization about a population based on information contained in a sample.

A sample is a characteristic or property of an individual population unit.

Definition 1.7

Following examples are for checking “Population, variable, sample, and Inference”.

We also need to know its reliability – that is, how good the inference is?

Thus, we introduce an element of uncertainty into our inferences.

Reliability is the fifth element of inferential statistical problems.

Definition 1.8

Four Elements of Descriptive Statistical problems

1. The population or sample of interest.

2. One or more variables that are to be investigated.

3. Tables, graphs, or numerical summary tools.

4. Identification of patterns in the data

Five Elements of Inferential Statistical Problems

1. The population of interest.
2. One or more variables that are to be investigated.
3. The sample of population units.
4. The inference about the population based on information contained in the sample.
5. A measure of reliability for the inference.

Definition 1.9

Examples for Quantitative data

1. The temperature;

2. The current unemployment rate for each of the 50 states;

3. The scores of a sample of 150 law school applicants on the LSAT;

4. The number of convicted murders who receive the death penalty each year over a 10-year.

Definition 1.10

Qualitative data are measurements that can not be measured on a natural numerical scale; they can only be classified into one of a group of categories.

Examples for Qualitative data

1. The political party affiliation (Democratic, Republican or Independent) in a sample of 50 voters;

2. A taste-tester’s ranking (best, worst, etc.) of four brands of barbecue sauce for a panel of 10 testers.

Obtain data in four different ways:

1. Data from a published source (book, journal, newspaper).

2. Data from a designed experiment.

3. Data from a survey.

4. Data from an observational study.

Definition 1.11

A random sample ensures that every subset of fixed size in the population has the same chance of being included in the sample.

Definition 1.12

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