Statistics Terminology

What is statistics? The science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data. Where might we use it? Sports, Real Estate, Stock Market, Health Field

Branches of Statistics Descriptive Statistics Consists of the collection, organization, summation, and presentation of data. Describing a situation. Example: Surveying a class and finding out each person’s favorite color then presenting the data. Inferential Statistics Consists of generalizing from samples to populations, performing hypothesis testing, determining relationships among variables, and making predictions. Making inferences from samples to populations. Example: Stores may look at previous year’s sales to determine what to order for current year.

Variables Variables: Attributes of a person or object. Examples: Gender, age, height, weight. Data: The actual value (measurement or observation) given to the variable. The collection of data creates a Data Set. Data value or datum: Each value in the data set. Population: Consists of all subjects that are being studied. Sample: A subgroup of the population.

Qualitative vs. Quantitative Qualitative Variables Variables that can be placed into categories, according to some characteristic or attribute. (Also called categorical) Examples: Hair color (Brown/Blonde) Gender (Male/Female) Political Affiliation (Rep./Dem./Indy) Quantitative Variables Variables that are numerical in nature and be ordered or ranked. Examples: Weight (54 pounds, 25 grams) Age (15 yrs., 67 yrs.) Broken down into 2 more sub categories. Discrete and Continuous.

What do you think? Do you think the following are a quantitative variable or a qualitative variable? 1.Height 2.Age 3.A Speaker 4.Pizza 5.Intelligence

Discrete vs. Continuous Discrete Variables: Values that can be counted. Must be integer in nature. Examples: Students in classroom, Pop. of Somerville and Branchburg, Place you come in during a race. Continuous Variables: Values that can be between any two specific values. Obtained by measuring. Examples: Weight 85 pounds (84.5 pounds – up to but not including 85.5 pounds) Height 71 inches (70.5 inches – up to but not including 71.5 inches)

Your turn What are some other types of discrete or continuous variables? Explain why.

Measurement Level of Variables Variables can also be classified by how they are categorized, counted, or measured. This type of classification uses measurement scales. Four common types of scales: 1.Nominal 2.Ordinal 3.Interval 4.Ratio

Nominal Level Classifies data into mutually exclusive, exhausting categories in which no order or ranking can be imposed. Examples: Political Affiliation, Religion, Gender, Marital status.

Ordinal Level Classifies data into categories that can be ranked but precise differences between the ranks do NOT exist. Examples: Evaluating a speaker as poor, good, or great. Evaluating the height of a person as short, medium, or tall.

Interval Level Ranks data but precise difference between the units DO exist. There is no meaningful zero. Examples: The IQ of an individual. There is a meaningful difference between IQ of 114 and an IQ of 115. Temperature. There is meaningful difference between 88* and 90*.

Ratio Level Has all the characteristics of Interval Level. A true zero DOES exist. Also true ratios exist when the same variable is measured on two different members of the population. This is the highest level of measurement. Examples: Height, Weight, Salary, Time

On what level? What level do the following fall into? 1.Teachers salary. 2.Cars driven by students. 3.Your grade in science. 4.The high temperatures this week.

Data Collection One of the most common ways to collect data is by use of surveys. The 3 most common are: 1.Telephone Survey 2.Mailed Questionnaire Survey 3.Personal Interview Survey Though surveys are the most common data can also be collected by conducting experiments, through a census, and also by direct observation.

Survey Advantages/Disadvantages Telephone advantages: Less costly than personal interviews. Also people may be more candid in their opinions if not face-to-face contact. Telephone disadvantages: Many people may not be home during the time of the call or may not pick up due to caller id.

Survey Advantages/Disadvantages Mailed questionnaire advantages: Can cover a larger geographic area than telephone or interview survey since they are less expensive. People can remain anonymous. Mailed questionnaire disadvantages: Low number of responses and inappropriate answers. Also some people may not be able to read or understand the questionnaire correctly.

Survey Advantages/Disadvantages Personal Interview advantages: Can obtain in- depth responses. Personal Interview disadvantages: Interviewers must be trained in asking questions and recording answers. Makes this the most expensive method. The interviewer may be biased on the people they select to interview.

Sampling When data is collected using samples, rather than a whole population, it is less costly and saves time. In order to obtain unbiased data statisticians use 4 basic sampling methods: 1.Random 2.Systematic 3.Stratified 4.Cluster

Random Sampling Random Samples are selected by chance methods or random selection. Give each subject a number, place it in bowl or hat, then begin selecting. Could lead to a biased sample rather easily. Statisticians may use computer programs or calculators to select numbers at random.

Systematic Sampling Systematic samples are obtained by once again numbering each subject. Rather than picking a number out of hat or bowl every kth number is selected. Example: 500 people in population and we need 50 people for sample. Therefore we will use every 10 th person. The first person, numbered 1 – 10 is chosen at random then every 10 th person from then on.

Stratified Sampling Researchers divide the population into smaller groups called strata. The characteristics of the groups are important to the study. A sampling from each group is then taken by randomly selecting the subjects. Example: Surveying freshman and seniors on their ease of getting around SHS.

Cluster Sampling Researchers use intact groups called clusters. This sampling technique is used when population is large or when the populations resides in a large geographic area. Example: Conducting a study using all the teachers in the state of NJ. Instead of asking each one the researcher will ask all the teachers in just a few districts of each county.

Convenience Sampling Researchers use subjects that are convenient. Example: A researcher stands on the corner of Main St. and Davenport (between 12 pm and 1 pm) and asks those passing by what their favorite pizza in town is. This sample is most likely not representative of the town’s population since those not walking in that part of town were not questioned.