Manuals/calci/SIGNTEST

SIGNTEST(Array,Median,AlternateHypothesis,LogicalValue)

• $Array$ is the set of values to find the statistic value.
• $Median$ is the median of the array of values.
• $AlternateHypothesis$ is the alternate hypothesis of the array.
• $Logicalvalue$ is either TRUE or FALSE.

Description

• This function gives the test statistic of the Sign test.
• The Sign Test is ued to test the Hypothesis that there is no difference between two continuous distributions X and Y.
• This test is one type of the Non parametric Test.
• The sign test is designed to test a hypothesis about the location of a population distribution.
• The Sign test does not require the assumption that the population is normally distributed.
• The normality of the distribution is doubtable, then Sign test is used to find the statitic instead of one sample T-test.
• The sign test uses the sign of the differences, unlike the paired t test which uses the sign and magnitude of the differences.
• To perform this test, Consider the independent pairs of sample data from the populations ${(x_{1},y_{1})(x_{2},y_{2}).....(x_{n},y_{n})}$.
• From this pair,it must be omitted with no differences $(x_{i}=y_{i})$.
• The Sign test data are having the following properties:
• 1.The differences of pairs are assumed to be independent.
• 2.Each pairs comes from the same continuous population.
• 3.The values $X_{i}$ and $Y_{i}$ represent are ordered , so the comparisons "greater than", "less than", and "equal to" are meaningful.
• The test statistic is expected to follow a binomial distribution, the standard binomial test is used to calculate significance.
• The sign test can also be viewed as testing the hypothesis that the median of the differences is zero.
• The sign test Hypothesis is having the following steps:
• Step1:State Null and Alternative Hypothesis
• Two ways to state these: One sample or sample of differences, want to test specific value for the population median M.
• Null: H0:p=1/2is equivalent to M = M0.
• Alternative: Ha:p<1/2 is equivalent to $M>M_{0}$ or $Ha:p>1/2$ is equivalent to $M<M_{0}$ or Ha:p not equal to 1/2 is equivalent to $M\neq M_{0}$
• Step2:Test statistic (no data conditions needed)
• S+ = Number of observations greater than $M_{0}$ or Number of observations with $x>y$.
• S− = Number of observations less than $M_{0}$ or Number of observations with $x<y$.
• Ties are not used, so use n = S+ + S−.
• Step3: Finding the p-value
• Remember, p-value is:
  • Probability of observing a test statistic as large as or larger than that observed
  • in the direction that supports Ha
  • if the null hypothesis is true.
• Step 4:Use tables of the binomial distribution to find the probability of observing a value of

r or higher assuming p = 1/2 and $n=n_{0}$.

• If the test is one-sided, this is your p-value.
• Step5: If the test is a two-sided test, double the probability to obtain the p-value.