Chapter 1:Introduction to Statistics

Reasons to Study Statistics• Statistics is prevalent in many fields, including the arts,

nursing, music, sports, business, and politics.• Statistics gives us a clearer understanding of the world

around us. It provides the methods and techniques for developing knowledge and for learning from information, thus forming the basis for thinking and planning ahead.

• Statistics allows us to formulate questions that can be addressed by using data and it provides the methods needed to adequately describe, summarize, analyze, interpret, and draw valid conclusions from the set of data to answer the questions.

• Example: Does anger lead to heart disease?

What is Statistics?• In general, statistics is a collection of methods

for gathering, organizing, summarizing, describing, analyzing, interpreting, presenting, and making valid conclusions of numerical data.

• Statistics deals with:– Designing the data collection process and

experiments– Preparing the data collected for analysis and to aid

understanding– Analyzing and drawing conclusions from data– Making estimates and predictions from data

Descriptive vs Inferential Statistics• The purpose of descriptive statistics is to make

the collected data more easily comprehensible and understandable, whereas the purpose of inferential statistics is to predict and make conclusions about the data.

• Descriptive statistics aim to describe what is going on in the data or what the data collected actually shows. There is no intention to make a conclusion. That is the job of inferential statistics.

Descriptive vs Inferential Statistics

• Some techniques descriptive statistics utilize to describe or summarize data:– Numerical counts or frequencies– Construction of tables and graphs– Computation of various descriptive measures such

as averages, percentages, and percentiles.– Computation of variability measures such as

range, variance, and standard deviations.

An Example of Descriptive StatisticsWho abuses and neglects children? In 2001, Child Protective Service (CPS) agencies investigated more than 3.25 million reports of child abuse and neglect throughout the United States. CPS investigations determine that 60% of the perpetrators in 2001 were female with an average age of 31, and 40% were male with an average age of 34. Approximately 84% were abused by a parent; Mothers alone were responsible for 47% of neglect and 32% of the physical abuse. 51% of all victims were White, 28% were African American, 18% were Hispanic, 2% were American Indian/Alaska Natives, and 1% were Asian/Pacific Islanders. Source: http://www.preventchildabuse.com/abuse.htm

More on Inferential Statistics• Inferential statistics deals with drawing conclusions,

making estimations, predictions, and generalizations about an entire set of data by studying only part of the data.

• An example:How many children die each year form child abuse? Based on data reported by CPS agencies in 2001, it is estimated that nationwide, 2000 children died as a result of abuse or neglect. Based on this number, five to six children die each day as a result of child abuse or neglect.Source: http://www.preventchildabuse.com/abuse.htm

Population vs Sample• A population is a complete collection of a set of

units such as people, objects, events, transactions, animals, plants, or other things whose characteristics a researcher is interested in learning about.

• Often times it is too time consuming or costly to study a whole population, so a sample of the population is taken.

• A sample is a collection of some, but not all of the elements of a population.

Population vs Sample• If you take two samples from the same

population, you likely will not get the same results. This is known as sampling variation or sampling error.

• Sampling variation decreases as the sample size increases.

• Samples must be based on a technique known as random sampling, meaning each member of the population has must have an equal chance of being selected. A sample based on this technique is known as a random sample.

Units of Analysis (Elements)

• A unit of analysis or an element is a single entity of the population from which information will be collected for analysis.

• In identifying the units of analysis, ask yourself the question “what things are being compared or examined by the researcher?”

Let’s look at an example:When examining the NJ gubernatorial race of 2009, Rasmussen ran a poll in May 2009 that reported Chris Christie at 47% and Jon Corzine at 38%. This was a statewide telephone survey of 500 likely voters, and had a margin of sampling error of +/- 4.5%.The population of interest:All registered voters in the State of NJThe units of analysis:Individual registered voters in NJThe sample:500 likely voters in NJ

Parameter vs Statistic

• A parameter is a numerical descriptive measure of a population, whereas a statistic is a numerical descriptive measure of a sample (think p-p and s-s).

• A parameter is a single value computed by using all the values in the entire population, whereas a statistic is a single numerical value computed by using only sample data.

• A census is a study in which all members of the population are included.

Example: The quarterly tax receipts were submitted to the Controller of Narwhal Township for the period ending June 2004 by all 56 business establishments in that locale. The average tax receipt was computer as $10,320. The value “$10,320” represents a:A) Sample B) StatisticsC) Parameter D) populationC. Parameter. $10,320 is a numerical description of the entire population (all 56 establishments).

Variables• A variable is a common characteristic that an

investigation focuses on after all the units of analysis in the population or sample underlying the study have been identified.

• A variable tells us what particular characteristic is being studied or is of interest to the researcher.

• For example, say our population is all USA citizens. They have many characteristics such as weight, age, height, gender, eye color, etc… Whatever you want to study is your variable.

• Values of variables can change across people, time, objects, space, or events. For example, weight constantly changes.

Example: What is the variable of interest?The reputations of many business can be severely damaged by shipments of manufactured items that contain a large percentage of defectives. A manufacturer of alkaline batteries wants to be reasonably certain whether fewer than 5% of its batteries are defective. To do so, 300 batteries are randomly selected from a very large shipment, each is tested and 10 defective batteries are found.The variable of interest is:Number of defective batteries

Values of a Variable

• A variable may consist of two or more values. • The variable gender has two values: male and

female.• Other variables like weight have many values.

Dependent and Independent Variables

• Let’s say our question to study is “why is it that some students prefer to sit in the back of the classroom and others prefer to sit in the front of the classroom?”

• The variable that constitutes the “why” question is our dependent variable. It is the variable we want to understand that is effected by some unknown cause.

• The dependent variable here would be seating preference, and the values of the variable would be front rows and back rows.

• Each why question (dependent variable) is looking for what causes the differences between the respondents on the variable.

• The causal explanation for the observed difference is the independent variable.

• What causes one student to sit in the front and one student to sit in the back?

• The independent variable is the variable that influences the behavior of other variables.

• An investigator may be able to alter, manipulate, or control the independent variable.

• The independent variable is sometimes called the input or predictor variable.

Here is an example linking crime rates to types of communities. Since the type of community may cause the crime rate, the type of community is the independent variable, and the crime rate is the dependent variable.

Control Variables• In conducting research, there may be other variables

could effect the dependent variable.• These variables need to be “controlled” or else they

can confused the interpretation of the research results.

• For example, say you want to test if expensive golf balls travel farther than cheap ones. Things other than cost of the golf ball may effect how far the ball travels, such as the golf club being used, the golfer, the weather, etc… It is important to control these variables, and perform the research using the same club, same golfer, and a neutral weather environment.

Hypothesis• A hypothesis is a testable statement about the

empirical relationship between the independent variable and the dependent variable (or between cause and effect).

• The hypothesis must indicate a predictable relationship between variables.

Examples:• Students from richer communities have higher

SAT scores than those from poorer communities.

• NFL teams have a greater ability to win games at home than they do on the road.

• Women are more likely to favor handgun permits than men.

In some sense, the hypothesis is your hunch, or what you believe is true.