What is statistics?
Data consists of information coming from observations, counts, measurements, or responses. The singular for data is datum.
STATISTICS is the science of collecting, organizing, analyzing and interpreting data in order to make decisions.
Population: The collection of all responses, measurements, or counts that are of interest.
Sample: A portion or subset of the population.
Parameter: A number that describes a population characteristic
ex: average age of all people in the United States
Statistic: A number that describes a sample characteristic
ex: average age of people from a sample of 3 states
Branches of Statistics
Descriptive Statistics: Involves organizing, summarizing and displaying data.
Inferential Statistics: Involves using sample data to draw conclusions about a population.
Data sets can consist of two types of data: qualitative data and quantitative data.
Qualitative data consists of attributes, labels, or nonnumerical entries.
Quantitative data consists of numerical measurements or counts.
Levels of Measurement
1. Nominal: Categories, names, labels, or qualities. Cannot perform mathematical operations on this data.
ex: type of care you drive, your major
2. Ordinal: Data can be arranged in order. You can say one data entry is greater than another.
ex: TV Ratings, condition of patient in hospital, student GPA
3. Interval: Data can be ordered and differences between 2 entries can be calculated. There is no inherent zero (a zero that means "none".)
ex: Temperature, year of birth
4. Ratio: There is an inherent zero. Data can ordered, differences can be found ad a ratio can be formed so you can say one data value is a multiple of another.
ex: Height, weight, age
Simple Random Sample: Each member of the population has an equal chance of being selected.
Assign a numer to each member of the population
Random members can be generated by a random number table, software, program of calculation
Members of the population that correspond to these numbers become members of the sample
Systematic Sample: Choose a starting value at random. Then choose every k+h member of the population
Convenience Sample: Choose readily available members of the population for your sample.
Stratified Sample: Divide the population into groups (strata) and select a random sample from each group.
Cluster Sample: Divide the population into individual units or groups and randomly select one or more units.
Experiment: Apply a treatment to a part of the group
Simulation: Use a mathematical model (often with a computer) to reproduce condition.
Census: A count or measure of the entire population.
Sampling: A count or measure of part of the population.
Designing a statistical Study
1. Identifying the variables of interest (the focus) and the population for the study.
2. Develop a detailed plan for collecting data. Make sure the data are representative of the population.
3. Collect the data
4. Describe the data with descriptive statistics techniques
5. Make decisions using inferential statistics. Identify any possible errors.