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==Feature==
<div style="font-size:25px">'''SIGNTEST(Array,Median,AlternateHypothesis,LogicalValue)'''</div><br/>
*<math>Array</math> is the set of values to find the statistic value.
*<math>Median</math> is the median of the array of values.
*<math>AlternateHypothesis</math> is the alternate hypothesis of the array.
*<math>Logicalvalue</math> 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{(x1,y1)(x2,y2).....(xn,yn)}.
*From this pair,it must be omitted with no differences(xi=yi)
*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 <math>X_i</math> and <math>Y_i</math> 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: <math>Ha:p<1/2</math> is equivalent to <math>M>M_0</math> or <math>Ha: p>1/2</math> is equivalent to <math>M < M_0</math> or Ha:p not equal to 1/2 is equivalent to <math>M\ne M_0</math>
*'''Step2''':Test statistic (no data conditions needed)
*S+ = Number of observations greater than <math>M_0</math> or Number of observations with <math>x>y</math>.
*S− = Number of observations less than <math>M_0</math> or Number of observations with <math>x<y</math>.
*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 <math>n = n_0</math>.
*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.