Stats 2500 Mun Chapter 1

What is Statistics?

1. Collecting Data (eg survey) 2. Presenting Data (eg Charts/tables 3. Characterising Data (Average) The data is analysed to help with decision making.

What are the two Statistical Methods?

1. Descriptive Statistics 2. Inferential Statistics

What are the Four Fundamental Elements?

1. Experimental unit • Object upon which we collect data 2. Population • All items of interest 3. Variable • Characteristic of an individual experimental unit 4. Sample • Subset of the units of a population

**What are two types of Data?**

1. Quantitative data are measurements that are recorded on a naturally occurring numerical scale. (Numeric scale, salaries, ages) 2. Qualitative data are measurements that cannot be measured on a natural numerical scale; they can only be classified into one of a group of categories. (categories, gender, method of payment)

Types of Random Samples

1. Simple Random Sample 2. Stratified random sample (used when units associated with the population can be separated in to two or more groups, called strata) 3. Cluster sample(natural groupings, clusters, of experimental units, like 10 restaurants out of 150) 4. Systematic sample(systematically selecting ever nth experimental unit, like every 5th customer) 5. Random response sample(Good for surveys where a question likely to be answered with a lie, have two questions, one being simple, the interviewer does not know which was answered, make the person more likely to tell the truth.)

*Five Elements of Inferential Statistical Problems*

1. The population of interest 2. One or more variables (characteristics of the population units) 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

**Four Elements of Descriptive Statistical Problems.**

1. The population or sample of interest 2. One or more variables (characteristics of the population or sample units) that are to be investigated 3. Tables, graphs, or numerical summary tools 4. Identification of patterns in the data.

Designed Experiment

A designed experiment is a data-collection method where the researcher exerts full control over the characteristics of the experimental units sampled. These experiments typically involve a group of experimental units that are assigned the treatment and an untreated (or control) group.

Define a Process.

A process is a series of actions or operations that transforms inputs to outputs. A process produces or generates output over time.

Process Black Box

A process whose operations or actions are unknown or unspecified is called a black box.

Simple Random Sample

A simple random sample of n experimental units is a sample selected from the population in such a way that every different sample of size n has an equal chance of selection.

Observational Study

An observational study is a data-collection method where the experimental units sampled are observed in their natural setting. No attempt is made to control the characteristics of the experimental units sampled. (Examples include opinion polls and surveys.)

Process Sample

Any set of output (object or numbers) produced by a process is called a sample.

Define Descriptive Stats

Descriptive statistics utilizes numerical and graphical methods to explore data, i.e., to look for patterns in a data set, to summarize the information revealed in a data set, and to present the information in a convenient form.

Importance of Selection

How a sample is selected from a population is of vital importance in statistical inference because the observed sample will be used to infer the characteristics of the sampled population.

Define Inferential Stats

Inferential statistics utilizes sample data to make estimates, decisions, predictions, or other generalizations about a larger set of data.

**Ways to Obtain Data**

Published source: book, journal, newspaper, Web site Designed experiment: researcher exerts strict control over the units Survey: a group of people are surveyed and their responses are recorded Observation study: units are observed in natural setting and variables of interest are recorded

**Nonrandom Sample Errors**

Selection bias results when a subset of the experimental units in the population is excluded so that these units have no chance of being selected for the sample. Nonresponse bias results when the researchers conducting a survey or study are unable to obtain data on all experimental units selected for the sample. Measurement error refers to inaccuracies in the values of the data recorded. In surveys, the error may be due to ambiguous or leading questions and the interviewer's effect on the respondent.

Statistical Thinking

Statistical thinking involves applying rational thought and the science of statistics to critically assess data and inferences. Fundamental to the thought process is that variation exists in populations and process data.

Define Statistics

Statistics is the science of data. It involves collecting, classifying, summarising, organising, analysing, and interpreting numerical information.