SIGNTEST(Array,Median,AlternateHypothesis,LogicalValue)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Array}
is the set of values to find the statistic value.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Median}
is the median of the array of values.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle AlternateHypothesis}
is the alternate hypothesis of the array.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {(x_1,y_1)(x_2,y_2).....(x_n,y_n)}}
.
- From this pair,it must be omitted with no differences Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X_i}
and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M>M_0}
or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Ha: p>1/2}
is equivalent to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M < M_0}
or Ha:p not equal to 1/2 is equivalent to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M\ne M_0}
- Step2:Test statistic (no data conditions needed)
- S+ = Number of observations greater than Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_0}
or Number of observations with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x>y}
.
- S− = Number of observations less than Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_0}
or Number of observations with
.
- 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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.
Example
Spreadsheet
|
A |
B
|
| 1
|
15 |
10
|
| 2
|
19 |
17
|
| 3
|
32 |
35
|
| 4
|
42 |
38
|
| 5
|
24 |
16
|
- =SIGNTEST(A1:B5,5,10,true)
TEST STATISTICS
SIGN TEST
| X Range |
Y Range |
Difference
|
| 15 |
10 |
5
|
| 19 |
17 |
2
|
| 32 |
35 |
-3
|
| 42 |
38 |
4
|
| 24 |
16 |
8
|
TEST STATISTICS
| P-Value |
0.375
|
Related Videos
See Also
References