# hypothesis

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```					  Module 5

Hypothesis testing
Hypothesis - What
• Null Hypothesis – A statement of status quo
which means no difference or no effect.

• Alternative Hypothesis – A statement where
some difference or effect is expected.
General Procedure for Hypothesis Testing
Formulate the null and alternative hypotheses

Select an appropriate test

Choose the level of significance

Collect data and calculate the test statistic

Check the critical value
Determine the probability      Compare         of the test statistic
associated with the test

Reject or do not reject null hypothesis
Errors in hypothesis testing
• Type I Error – Sample results lead to the rejection
of the null hypothesis when it is in fact true.
(probability of type I error denoted by α)

• Type II Error – Sample results lead to the
acceptance of the null hypothesis when it is infact
false. (probability of type II error denoted by β)
Hypothesis Tests

Parametric tests                               Non Parametric tests

One                   Two                          One                Two
Sample               Samples                       Sample            Samples
t test                                              Chi - square
z test                                              K-S
Runs
Independent         Paired                 Binomial                 Paired
Independent
Two group           Paired t                                    Sign
t test              test                     Chi - square       Wilcoxon
z test                                       Mann - Whitney     McNemar
Median             Chi - Square
K-S
Parametric Tests

• Parametric tests assume that the variables pf
interest are measured on at least an interval
scale.

• Provide inferences about means of parent
populations
t - test
• T statistic used for making inferences about
the parent populations.

• T – test: Assumes that the variable is normally
distributed, with μ mean, population variance
σ² is unknown
• Population variance is estimated from the
sample s².
T - Test Cont…
• T distribution similar to normal but with more
area under the tails and less under the peak

• T distribution approaches normal distribution
as degrees of freedom increase.

• For samples of 120 or more, t and normal
distributions are mutually indistinguishable.

• Degree of freedom = n-1
Z test
• Z test is conducted in case of normal
distributions

• The population standard deviation is assumed
to be known in this case
F test
• F Test is conducted in case of comparison of
two independent samples. (eg. Difference
between users and non users)

• An F test of sample variance may be
conducted if it is not known if the two
populations have equal variance.
Non Parametric tests

• Non Parametric tests assume that the
variables of interest have been measured on
nominal or ordinal scales

• Tests are available for
– One ; Two (independent or paired tests)
U test (Mann – Whitney’s U)
• Used in case of two independent samples

• Used when the difference in the location of the two
populations is to be compared based on two
independent samples

• Samples are combined and cases ranked in ascending
order. If the samples are from the same population,
their distribution should be random.
Rank Sum test – Wilcoxon test

• Used in case of paired samples

• Test analyses the differences of the between paired
observations taking into account the magnitude.

• Computes the differences and ranks the differences.
• In case of no difference the ‘Z’ statistic is a standard
normal variate with mean 0 and variance 1
KW test (Kruskal Wallis test)
• It is a non parametric test for comparing
population medians.

• Tests the null hypothesis that k samples from
possibly different populations actually
originate from the same population.
KW test procedure
• Each observation in K samples replaced by its
rank with smallest observation getting 1 and
greatest N (N= total sample size of k samples)

• Sum of ranks is computed for each sample.

• KW determines whether the sums are
different enough for the samples to have
come from different populations

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 views: 55 posted: 1/25/2011 language: English pages: 15