Statistics

Statistics

1. science of collecting, describe, analyse and interpret data

   • Basic Concepts
     • Population
       • totality of elements under consideration
     • Sample
       • Portion of population that is selected for analysis
     • Parameter
       • measure of overview that is calculated to describe a characteristic of a population.
     • Statistic
       • measure of overview that is calculated to describe a characteristic of a single sample of the population
     • Random Variables
       • phenomena which is dealed in the several questions developed by the statistician
       • 2 types
         • Qualitative
           • produce categorical responses
         • Quantitative
           • produce a numerical answer; quantify an element of the population.
             • Discrete Data
               • numerical responses arising from a process of counting
             • Continuous Data
               • responses arising from a process of measurement
   • Measures of Position
     • Z-score
       • subtraction of the number minus the mean divided by the standard deviation
     • Decile
       • (D1, D2, D3.....D10) .10 ea
     • Quartile
       • (Q1,Q2,Q3,Q4) .25 es
     • Percentile
       • 1%-100%
     • Box Plot

2. Descriptive Statistics

   • collection, organization, overview and presentation of sample data

3. Inferential Statistics

   • obtaining inferences or conclusions based on info taken from the samples

4. Measurement Scales

   • Properties
     • Identity
       • Each value on the measurement scale has a unique meaning
     • Magnitude
       • values have an ordered relationship to one another
     • Equal Intervals
       • Scale units are equal to one another
     • Minimum value of zero
       • The scale has a true zero point.
   • Types
     • Nominal
       • Identity
     • Ordinal
       • Identity and Magnitude
     • Interval
       • identity, magnitude and equal intervals
     • Ratio
       • Identity, magnitude, equal intervals and minimum value of zero

5. Sampling Methods

   • Population Parameter
     • true value of a population attribute
   • Sample Statistics
     • estimate, based on sample data of a population parameter.
     • 2 categories
       • Probability samples
         • each element has a chance of being chosen
           • Simple random sampling
             • the population has N objects, the sample has n objects, all samples of n are equally likely to occur
           • Stratified sampling
             • the population is divided into groups, based on some characteristic, this groups are strata.
           • Cluster sampling
             • every member of the population is assigned to one group, cluster.
           • Multistage sampling
             • combination of different sampling methods
           • Systematic random sampling
             • we create a list of the population, randomly select the sample element from the first k elements, we select kth elements.
       • Non-probability samples
         • we don´t know the probability that each element will be chosen
           • Voluntary sample
             • people who self-select into the survey
           • Convenience sample
             • people who are easy to reach

6. Visual Displays of Data

   • Displays
     • Line Graphs
     • Circle Graphs
     • Bar Graphs
     • Stem and leaf
     • Histogram
   • Frequency Distribution
     • frequency
       • # of times the corresponding item occurred in the set data
     • relative frequency
       • fraction of the data set represented by the item
     • Grouped frequency distribution
       • lower class limits, upper class limits, class width, class mark

7. Measures of Dispersion

   • Range
     • highest value - lower value
   • Standard Deviation
     • addition of the square of the value less the mean divided by the total number of elements minus one, square root of the result
   • Coefficient of variation
     • standard deviation divided by the mean
   • Chevyshev´s rule
     • 1-1/K^2 (k is the # of stander deviations