# Introduction to Statistics FSE 200 Statistics Statistics are

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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 v. Used to organize and describe the characteristics of a particular data set v. Example: the average 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 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!!!!!!

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. 2. 3. 4. Exploration Description Explanation 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 intervallevel 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 Level Nominal Ordinal Classifies Ordered Numbers Objects from have High to equal Low intervals X X X Interval X X X Ratio X X X Numbers have a theoretical zero point X

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.