BASIC STATISTICS
STATISTICS-Collection of methods for
planning experiments, obtaining data, and
then organizing, summarizing, presenting,
analyzing, interpreting, and drawing
conclusions based on the data.
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The core of statistics, variables, population, and sample. It also discusses various types of variables, such as numerical and non-numerical data, and different levels of data, such as nominal, ordinal, and interval levels. The document also highlights the abuses of statistics and two common sources for statistical methods, observational study and experiment. Finally, it explains five common types of sampling, including random, stratified, and systematic sampling.
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BASIC STATISTICS
STATISTICS -Collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.
THE CORE OF STATISTICS
VARIABLE - Attribute that can assume different values.
- (^) Variables are comprised of data. If the data is chosen by chance, we have random variables. (^) POPULATION -Complete collection of all elements to be studied. (^) SAMPLE -Subcollection of elements drawn from a population.
- (^) Example: Taking a sample of teenage girls to find out who is going to prom. Then, using the results to make a conclusion about the entire population of teenage girls in the high school going to prom.
DESCRIBING, EXPLORING, AND COMPARING DATA One area of statistics is descriptive statistics which is a method used to summarize or describe the important characteristics of a known set of population data. It consists of the collection, organization, summarization, and presentation of data. This differs from inferential statistics which is used to make inferences about a population from a sample data.
VARIOUS VARIABLES
We will try to understand the different levels of data to determine the best procedure needed to do statistical analysis. First, we must break data into two categories: numerical (ages, weights, years) vs nonnumerical (colors, sizes, types of crops).
NONNUMERIC DATA
QUALITATIVE DATA -can be separated into different categories that are distinguished by some nonnumeric characteristic.
- (^) Examples could be gender, car types, dog species.
INDEPENDENT VS
DEPENDENT
INDEPENDENT VARIABLE
- (^) Variable that researcher controls or chooses (^) Choose schools, type of instruction, type of exercise DEPENDENT VARIABLE
- (^) Resulting Variable-usually a measurement
NOMINAL LEVEL
Data consists of names, labels, or categories. Data cannot be arranged in an ordering scheme. Calculations at this level are not performed. Examples: survey responses, gender of students in classroom
ORDINAL LEVEL
Data can be arranged in some order, but differences between data values cannot be determined or are meaningless. Examples: Can’t find difference between things like ‘good’ and ‘bad.’
RATIO LEVEL
Interval level modified to include the zero starting point. Examples: lengths in movies, checking mpg, amount of trash discarded by households
USES OF STATISTICS
Government Industry Pharmaceutical Companies Education Analysis of Various Problems
- (^) Teen Pregnancy
- (^) Farm Depletion
- (^) Drunk Driving
EXAMPLES OF ABUSES
Small Samples Precise Numbers – not always accurate
- (^) Precise-all in the same area, but not necessarily in the right place
- (^) Accurate-putting the dart in the bullseye Guesstimates Distorted Percentages-misleading or unclear percentages Partial Pictures
Deliberate Distortions Loaded Questions Misleading Graphs-can exaggerate or de- emphasize the true nature of data Pictographs-drawings of objects Pollster Pressure Bad Samples-inappropriate methods for collecting data
STEPS FOR DESIGNING A STUDY
YIELDING VALID RESULTS
Identify the exact question to be answered and the relevant population. Develop a plan for collecting data. Collect the data. Analyze the data and draw conclusions identifying possible sources of errors.
TWO COMMON SOURCES FOR
STATISTICAL METHODS
(^) OBSERVATIONAL STUDY -observe and measure specific characteristics but don’t attempt to manipulate or modify the subjects being studied.
- (^) Collecting data without modifying the people being polled such as the number of students who would see a recreational facility beneficial to the school. (^) EXPERIMENT -apply some treatment and proceed to observe its effects on the subjects
- (^) Performing a modification on the subjects before the observation begins. An example might be giving the subjects a drug to increase productivity.