Modular 1

Introduction of the Course Structure and MyLabsPlus

Ch 1.1 & 1.2 Basic Definitions for Statistics Objective A : Basic Definition Objective B : Level of measurement of a Variable Objective C : Observational Study versus Designed Experiment

Ch 1.1 & 1.2 Basic Definitions for Statistics A1. Definition Statistics is the science of collecting, organizing, summarizing, and analyzing data to draw conclusions. Descriptive statistics consist of collecting, organizing, summarizing, and presenting data. Inferential statistics consists of generalizing from samples to populations, performing estimations and hypothesis tests, and making predictions. Objective A : Basic Definition What is Statistics? Statistics Descriptive Statistics Inferential Statistics

A parameter is a numerical summary of a population. A population consists of all individuals (person or object) that are being studied. A statistic is a numerical summary of a sample. A sample is a subset of the population. Population versus Sample Parameter versus Statistic

Identify the population and sample in the study. Example 1: A farmer wanted to learn about the weight of his soybean crop. He randomly sampled 100 plants and weighed the soybeans on each plant. Example 2: Determine whether the underlined value is a parameter or a statistic. (a) Only 12 men have walked on the moon. The average age of these men at the time of their moonwalks was 39 years, 11 months, 15 days. (b) In a national survey on substance abuse, 66.4% of respondents who were full-time college students aged 18 to 22 reported using alcohol within the past month. Population – Sample – Parameter. Statistic. All soybean plants planted by the farmer. 100 randomly selected soybean plants.

A2. Variables and Type of Data Qualitative (categorical) variables are variables that can be placed into distinct categories. Quantitative (numerical) variables are numerical and arithmetic operations can be performed. A discrete variable can assume a countable number of values. A continuous variable can assume an infinite number of values between any two specific values. They often include fractions and decimals. A variable is a characteristic that can assume different values called data. Variable Qualitative versus Quantitative Variable Quantitative variable Discrete variable Continuous variable

Example 1: (a) Number of students attending a university for Fall (b) Colors of football caps in a store. Classify each variable as qualitative or quantitative. If the variable is quantitative, further classify the data as discrete or continuous. (c) Social security number. Qualitative Discrete Quantitative Qualitative (d) Water temperature of a swimming pool. Continuous Quantitative

Ch 1.1 & 1.2 Basic Definitions for Statistics Objective A : Basic Definition Objective B : Level of measurement of a Variable Objective C : Observational Study versus Designed Experiment

Objective B: Level of measurement of a Variable Four common types of measurement scales are used: nominal, ordinal, interval, and ratio. The nominal level of measurement classifies data into categories in which no order or ranking can be imposed on the data. For example: Eye color The ordinal level of measurement classifies data into categories that can be ranked. For example: Course grade In addition to being classified as qualitative or quantitative, variables can be classified by how they are categorized, counted, or measured. Ch 1.1 & 1.2 Basic Definitions for Statistics

The ratio level of measurement ranks data, differences in the values or the variable have meaning, and there exists a true zero. The interval level of measurement ranks data and differences in the values of the variable have meaning. Also there is no true zero. For example: Sea level; Temperature For example: Length

Ch 1.1 & 1.2 Basic Definitions for Statistics Objective A : Basic Definition Objective B : Level of measurement of a Variable Objective C : Observational Study versus Designed Experiment

Definition In an observational study, the researcher observes the behavior of the individuals without trying to influence the outcome of the study. In a designed experiment, the researcher controls one of the variables and tries to determine how the manipulation influences other variables. The independent variable which is also called the explanatory variable in a designed experiment is the one that is being controlled by the researcher. The dependent variable which is also called the response variable is the resultant variable. Ch 1.1 & 1.2 Basic Definitions for Statistics

Confounding in a study occurs when the effects of two or more explanatory variables are not separated. A lurking variable is an explanatory variable that was not considered in a study, but that effects the value of the response variable in the study.

Example 1: (a) Rats with cancer are divided into two groups. One group receives 5 mg of a medication that is thought to fight cancer, and the other receives 10 mg. After 2 years, the spread of the cancer is measured. (b) Conservation agents netted 320 large-trout in a lake and determined how many were carrying parasites. Determine whether the study depicts an observational study or an experiment. An experiment An observational study

Example 2: (a) Rats with cancer are divided into two groups. One group receives 5 mg of a medication that is thought to fight cancer, and the other receives 10 mg. After 2 years, the spread of the cancer is measured. (b) A researcher wants to determine whether young couples who marry are more likely to gain weight than those who stay single. Identify the explanatory variable and the response variable for the following studies. Explanatory variable – Response variable – Explanatory variable – Response variable – the amount of medication dosage measure of the spread of the cancer marital status weight gained