Statistics

Statistics

1. descriptive

   • collection, organization, overview and presentation of sample data

2. inferential

   • conclusions about populations based on information taken from the samples.

3. A population (or universe) is the totality of the elements or things under consideration.

4. A sample is the portion of the population that is selected for analysis.

5. A parameter is a measure of overview that is calculated to describe a characteristic of a population.

6. random variables.

   • The data (required info.) can be conceived as numerical information necessary to help us make decisions with more bases in a particular situation. The survey statistician develops instruments that contain several questions dealing with a diversity of phenomena or characteristics.
     • Qualitative random variables produce categorical responses, i.e., to describe an element of a population.
     • Quantitative random variables produce numerical answers; quantify an element of the population.
       • Discrete
         • numerical responses arising from a process of counting
       • continuous
         • responses arising from a process of measurement

7. science of collecting, describe, analyze, and interpret data

   • A statistic is a measure of overview that is calculated to describe a characteristic of a single sample of the population.

8. Measurement Scales

   • Nominal
     • only satisfies the identity.
   • Ordinal
     • identity and magnitude.
   • Properties
     • Magnitude
       • Values on the measurement scale have an ordered relationship to one another. That is, some values are larger and some are smaller.
     • Equal intervals
       • Scale units along the scale are equal to one another. This means, for example, that the difference between 1 and 2 would be equal to the difference between 19 and 20.
     • A minimum value of zero
       • . The scale has a true zero point, below which no values exist.
     • Identity
       • Each value on the measurement scale has a unique meaning.
   • Interval
     • identity, magnitude, and equal intervals.
   • Ratio
     • identity, magnitude, equal intervals, and a minimum value of zero.

9. Sampling Methods

   • way that observations are selected from a population to be in the sample for a sample survey.
     • A population parameter is the true value of a population attribute.
     • A sample statistic is an estimate, based on sample data, of a population parameter.
   • Probability samples
     • each population element has a known (non-zero) chance of being chosen for the sample.
       • Simple random
       • Stratified
       • Cluster
       • Multistage
       • Systematic random
   • Non-probability samples
     • we do not know the probability that each population element will be chosen, and/or we cannot be sure that each population element has a non-zero chance of being chosen.
       • Voluntary
       • convenience

10. Frequency distributions

    • lists the distinct data values(x) along with their frequencies(f)
      • Relative frequency
        • Fraction or percentage of the data set represented by the items
      • Group frequency
        • 1.Make sure each date will fit into ONE class 2.Try to make all the classes the same width 3.Make sure the classes don't overlap 4.Use from 5 to 12 classes
      • Stem-and-Leaf Displays
      • Graphs
        • Bar Graphs
        • Line Graphs
        • Circle Graphs

11. Measures of central tendency

    • Median
      • Its not sensitive to extreme values. Divides a group of numbers into 2 parts, half below the median and half above it
    • Mode
      • Data set of the value that occurs most often
    • Mean
    • Weighted Mean

12. Measures of dispersion

    • Range
      • (Greatest value in the set) - (least value in the set)
    • Standard Deviation
    • Chebyshev's theorem
    • Coefficient of variation
      • For sample
      • For population

13. Measures of position

    • Z-score
    • Quartile
      • the three values (Q1, Q2 AND Q3) that a data set into four (approximately) equal-sized parts.
    • Percentile
      • If aprox. n% of the items in a distribiution are less than the number n, then x is the nth percentile of the distribution
    • Decile
      • nine values (denoted D1, D2,..... D3) along the scale that devide a data set into ten (approximately) equal-sized parts
    • Box plot

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