Statistics
- science of collecting, organizing, summarizing and analyzing information to draw conclusion or answer questions.
- Provides a measure of confidence in any conclusion
Population
- the collection of all of the people or objects that one considers
Individual
- a single person of object of the population
Sample
- a subject of the population (a group of individual of the population) Descriptive statistics
- describes data through numerical summaries,tables and graphs Example
Inferential statistics
- uses methods that take a result from a sample,extend to the population, and measure the reliability of the result
One wants to conduct a statistics of HWCʼs students on whether they will study outside school. He or she thus then asked 10 students at the school.
Population : All students at the school
Individual : One of the 100 students asked
Sample : 100 students that are asked
Suppose 20 students said they wouldn't study at all outside school.
Descriptive statistics : 80% of the 100 students study outside school
Inferential statistics : It is confident to say that all students at school who would study outside school is 80%
Qualitative
(categorical) variables
- allows for classification of individuals based on some attribute or characteristic
Gender,Zip code
Quantitative variables
- provides numerical measures of individuals
- Arithmetic operations can be performed on the values of a quantitative variable and provides meaningful result
Temperature
Qualitative data
- Observations corresponding to a qualitative variable
Gender(M/F),Zip code(60616,90210)
Definition
Example
Quantitative data
- Observations corresponding to a quantitative variable
Temperature (17ʼC)
Nominal level of measurement - A variable has a nominal level of measurement if it names, labels or categorizes the individual
Gender,Race
Ordinal level of measurement - A variable has a ordinal level of measurement if there is a ranking or ordering
Grade of my GPA
Interval level of measurement - A variable has an interval level of measurement if it makes sense to add and subtract
Price, Temperature
Ratio level of measurement - A variable has a ratio level of measurement if itʼs numerical and it makes sense to divide one by the other to form ration.
Numbers of books of elderly citizens of the numbers of books the entire amount of all citizens Validity
- Represents how close to the true value the measurement is
The use of pH paper or the use of electric pH indicator will results in different acidic value. Reliability
- Represents the ability of different measurements of the same individual to yield the same results
Hawthorne experiment
Explanatory variable
Any variable that explains the response variable. Often called an independent variable or predictor variable.
Response variable
- The outcome of a study. A variable you would be interested in predicting or forecasting. Often called a dependent variable or predicted variable.
Explanatory : Whether people are obsese or not
Response: People consume how many soda Definition
Example
Observational study
- Measures the value of the response variable without attempting to influence the value of either the response or explanatory variables.
- Observes the behavior of the individuals in the study without trying to influence the outcome of the study
- Researchers observe whether people will pay their train fares under the honest system in Minneapolis
Designed experiment
- A researcher assigns the individuals in a study to a certain group,intentionally changes the value of the explanatory variable and then records the value of the response variable for each group.
- Researchers controls different amount of pop to see the relation of it to obesity
Confounding
- Occurs when an explanatory variable that separate the link
Lurking variable: family history
A lurking variable
- An explanatory variable that was not considered in a study, but that affects the vale of the response variable in the study.
Simple random sampling - The chance of every possible sample is equally likely to occur
Drawing sample with a blind-fold on
Systematic sample
- Obtained by selecting every x-th individual from the population
Drawing the most two youngest students of each class.
Cluster Sample
- Obtained by selecting all individual within a randomly selected collection or group of individuals
Convenience Sample
- A sample in which the individuals are easily obtained and not based on randomness
Confounding : people exercise or not
Asking people from my neighborhood to study the amount of electricity use