theory

• Descriptive Statistics


  refers to the calculation or presentation of figures to summarize or characterize a set of data
• Inferential Statistics


  relates to the case when sample descriptions are used to generalize some information about the population
• Population


  collection of measurements made from a set of entities under study; collection of entities under study
• Sample


  part of the population
• Random Sample


  part of a population such that every unit has the same chance of being selected
• parameter


  a measure that characterizes a population (usually unknown)
• Statistic


  a measure that characterizes a sample
• Parametric Tests

  • Tests about the population parameters
  • Based on specific assumption that the population where the sample came from a normal distribution
• Parametric Test

  • Tests about the population parameters
  • Based on specific assumption that the population where the sample came from a normal distribution
  • Scale of measurement should be at least interval. (interval/ ratio)
• Most inferential statistics assume normal distributions.
• Extreme deviations from normality can distort the results of these tests.
• The usual effect of violating the normality assumption is decrease in the Type I error rate (sounds like a good thing), but it often is accompanied by a substantial decrease in the power of the test.
• Non-parametric Tests

  • The form of the joint distribution is not assumed.
  • Test and estimation procedures require relatively fewer assumptions about the population distribution.
  • Usual assumption is that the random variables are independently and identically distributed.
• Distribution free test


  use methods that are based on functions of the sample observations whose corresponding random variable has a distribution which does not depend on the specific distribution function of the population from which the sample was drawn
• Non-parametric test


  tests for a hypothesis which is not about parameter values
• Why study non parametric test

  • In many applications, there is no prior knowledge of the underlying distributions.
  • If the parametric assumptions are violated, its use can give misleading or wrong results.
  • For studies with small sample sizes, the normal approximation does not work well.
• Non parametric tests are statistical methods that:

  • require very little model/distributional assumptions
  • robust/ sensitive to model/distributional assumptions
  • are sensitive to outliers in the data
• Advantages of non parametric tests

  • Generally quick and easy to apply
  • Tests of hypotheses which are not statements about parameter values have noncounterpart in parametric statictics
  • Test statistic is mostly discrete in nature and its exact sampling distribution can often be determined by permutation or combinatorial formulas.
• Advantages of non parametric tests

  • Little problem of violating assumptions and less chance for inappropriate application
  • May be applied when data are measured at a low scale of measurement, as for count data and ranks
  • Process of collecting and compiling sample data may be less expensive and less time consuming
• Disadvantages of non parameteric test

  • Non-parametric tests are sometimes used when parametric procedures are more appropriate
  • They are difficult to compute by hand for large samples
  • Statistical tables are not widely available.
• When to use non parametric tests

  • The hypothesis to be tested does not involve a population parameters
  • The data have been measured in a scale weaker than that required for the parametric procedure to be employed.
• When to sue non parametric tests

  • the hypothesis to be tested does not involve are not met.
  • Results are needed in a hurry and a computer is not readily available, and calculations must be done by hand (small sample sizes)
• • Parametric tests are often derived in such a way that power is satisfied for an assumed specific probability distribution.
• Non-parametric tests are inherently robust
• Non-parametric tests, whenever they are applicable, are a great convenience but their use must be strictly evaluated
• It is only after the use of a parametric test is carefully ruled out that the use of a nonparametric test is justified.