Introduction to Statistics FSE 200

Statistics “Statistics are like clothing. What they reveal can be suggestive, but what they conceal is vital.” Aaron Levenstein (slightly modified) “There are three kinds of lies: lies, damn lies, and statistics.” Benjamin Disraeli

Statistics: What It Is (and Isn’t) Statistics is “the science of organizing and analyzing information to make it more easily understood.” The class will help you learn how to conduct the following with data: –Collect –Organize –Summarize –Interpret

Descriptive or Inferential? Descriptive statistics  Used to organize and describe the characteristics of a particular data set  Example: the average age of everyone in this class Inferential statistics –Used to make inferences from your sample to the larger population Example: comparing the mean age of students taking this course to the average age of all students in an introductory statistics course

Descriptive Statistics Statistics concerned with summarizing the properties of a sample of observations These statistics typically describe the typical values and amount of variation in a value’s variables Frequencies, Mean, and Median are all descriptive statistics

Inferential Statistics Statistics that apply the mathematical theory of probability to make decisions about the likely properties of populations based on sample evidence If a sample is representative of the population, then inferences about the population can be made from the sample

Why Statistics Is Important Understanding basic statistics will help you in the following ways: –Better prepare you for advanced courses (both undergraduate and graduate) –Sets you apart from those who do not take courses in statistics –Challenges you intellectually –Makes you a better student in the sciences

Success in This Course A few hints for successful completion of this course: –Don’t skip lessons –Form a study group –Ask questions –Work through the exercises in each chapter –Look for real-world applications –Practice!!!!!!

MORE INFORMATION

Population v. Sample A population is the entire set of persons, objects, or events that has at least one common characteristic of interest to a researcher A sample is a subset of cases or elements selected from a population

Four Purposes of Research 1.Exploration 2.Description 3.Explanation 4.Applied/Evaluation

Exploration Exploratory projects collect data on some process to establish a baseline against which future changes will be compared. Most research topics begin with exploratory research when very little is known about the topic Exploratory studies are also appropriate when a policy change is being considered

Description Descriptive projects describe the scope of justice and safety problems or policy responses to those problems. Descriptive research strives to be more accurate than casual observations people make about social issues. Descriptive studies are concerned with counting or documenting observations The Uniform Crime Report produced by the FBI is an example of a descriptive study Results must be generalizable.

Explanation Much of the research found in the social scientific journals is explanatory research, or research seeking to explain why individuals participate in the behavior that they do.

Applied/Evaluation Research Evaluation research is used to determine the effectiveness of a program or policy

Variables Characteristics that vary in quality and or quantity among individuals Variables take on values that describe quality (e.g., the variable gender has the qualities of male or female) or quantity (the variable number of fires in a town may range from 0 to 50 in one year)

Attributes Qualities or quantities that describe the variable Male and female are attributes of the variable gender 0,1,2, and every number up to 50 are attributes of the variable number of fires in a town

Qualitative v. Quantitative Variables Qualitative variables consist of attributes that vary in quality or kind – The variable type of fire is a qualitative variable; fires may occur in residential, commercial, or wildland settings Quantitative variables are those that vary in degree or magnitude – The number of wildland fires in the U.S. in a single year is a quantitative variable

4 levels of Measurement Nominal Ordinal Interval Ratio

Nominal Level of Measurement The crudest level of measurement. Nominal measurement allows you to classify units of analysis into categories which are– mutually exclusive and exhaustive Nominal measures merely offer names or labels for characteristics. (Examples–sex, race, political preference, etc.).

2 Qualities all Variables Must Have Exhaustive – There should be a sufficient number of categories so that you can classify every observation in terms of one of the attributes composing the variable (types of fire might be commercial, wildland, residential, other). Mutually Exclusive – You must be able to classify every observation into one and only one category (firefighters are either (1) volunteer or (2) career or (3) both; some may be career firefighters who volunteer at a local department)

Ordinal Level of Measurement Ordinal measurement allows you to classify units of analysis into categories which are mutually exclusive and exhaustive. It also allows you to rank-order categories This additional category allows you to imply differences of degree and type. Numerals represent only the rank order of the variable. Ordinal categories in the social sciences are often treated as interval categories. Ex. (types of fire trucks- large, medium, small).

Interval Level of Measurement Allows the classification of units of analysis into categories which are mutually exclusive, exhaustive, rank-ordered and Numerals represent an equal amount of difference on the attribute being measured. Numerals represent not only rank order, but also allow you to express quantitative differences in amount. There is, however, an absence of an absolute or nonarbitrary zero point. Fear of arson measured on a 10-point scale is an interval- level variable

Ratio Level of Measurement Allows the classification of units of analysis into categories which are mutually exclusive, exhaustive, rank-ordered, and where numerals represent an equal amount of difference on the attribute being measured. In this type of measurement, there is also an absolute or nonarbitrary zero point. This makes it possible to multiply and divide scale numbers meaningfully and thereby form ratios. Examples include years of education, dollar amounts, age, number of prior arrests, etc.

Levels of Measurement Conclusion As a general rule, the more precise your measurement is, the better. Thus, given the choice, you would prefer measurement at the ratio level to measurement at the nominal level. In many situations, however, you don’t have a choice.

Levels of Measurement LevelClassifies Objects Ordered from High to Low Numbers have equal intervals Numbers have a theoretical zero point NominalX OrdinalXX IntervalXXX RatioXXXX

Causal relationship A causal relationship is one in which a change in one event produces a change in another Unless empirical generalizations have a theoretical explanation, scientists do not consider them causal relationships Explanation in social science thus boils down to a search for causes

Hypothesis A statement regarding the effect or influence of one variable on another variable.

Independent and Dependent Variables An independent variable is a variable that produces a change in another variable, usually appearing first in a hypothesis A dependent variable is a variable that is influenced, or affected, by the independent variable

Examples of Hypotheses Hypothesis 1- Male firefighters will be more likely than female firefighters to die of a heart attack while employed as a career firefighter. – Here, the gender of the firefighter is the independent variable where the likelihood of death due to a heart attack is the dependent variable. Hypothesis 2- The rate of heart attacks among volunteer firefighters will be higher than the rate of heart attacks among career firefighters. – Here, the employment status of firefighters is the independent variable and the likelihood of death due to a heart attack is the independent variable.