QM Week 3
the null and alternative for sign test is the same is
wilcoxon rank sum test
So instead of testing for the mean of ordinal data, we test for ... These techniques are called....
the location. these techniques are non parametric
How to calculator sign test test statistic (3)
1. calculate each difference 2. count positive differences 3. Count total of positive differences. This is T or X.
In order to use the normal apprxomination for the sign test (binomial distribution), the population must have greater than __ observations
10
For wilcoxon rank sum test, if we have large samples (>?), we do approximately normal distribution
30
If the alternative of the wilcoxon rank sum test is, the location of population A is different to the location from pop B, what is the decision rule (NORMAL APPROXIMATION)
Reject null if z is < or > than the critical value
If the alternative of the wilcoxon rank sum test is, the location of population A is to the right of the location from pop B, what is the decision rule (NOT NORMAL APPROXIMATION)
Reject H0 is T is greater than OR EQUAL TO Tupper
If the alternative of the wilcoxon rank sum test is, the location of population A is different to the location from pop B, what is the decision rule (NOT NORMAL APPROXIMATION)
Reject H0 is T is greater than OR EQUAL TO Tupper or if T is less than OR EQUAL TO Tlower.
If the alternative of the wilcoxon rank sum test is, the location of population A is to the right of the location from pop B, what is the decision rule (NORMAL APPROXIMATION)
Reject null if z>critical value
If the alternative of the wilcoxon rank sum test is, the location of population A is to the left of the location from pop B, what is the decision rule (NOT NORMAL APPROXIMATION)
Reject H0 is T is less than OR EQUAL TO Tlower
Problem Objective: Data type: Design: Test statistic <30 and >30: Null:
Problem Objective: Compare two populations Data type: Numerical and non-normal Design: Matched Pairs Test statistic <30: T+ (rank sum of the differences) Test statistic>30: Z-test Null: The location of population A is the same as the location of population B
Wilcoxon Rank Sum Test Problem Objective: Data type: Design: Test statistic n<10: Test statistic n>10: Null: Alternative: Required condition:
Problem Objective: Compare two populations Data type: Ordinal or Numerical but non-normal Design: Independent Test statistic n<10: T=TA (sum of rank of objective in column A) Test statistic n>10: Z-test Null: The location of population A is the same as the location of population B Alternative: Check notes Required condition: The two population distributions are identical in shape and spread
If the alternative of the wilcoxon rank sum test is, the location of population A is to the left of the location from pop B, what is the decision rule (NORMAL APPROXIMATION)
Reject H0 if z < critical value
Sign Test Problem Objective: Data type: Design: Test statistic: Null:
Sign Test Problem Objective: Compare two populations Data type: Ordinal or Numerical but non-normal Design: Matched Pairs Test statistic: Z-Test using T+ as x in formula on formula sheet Null: The location of population A is the same as the location of population B
Requirement of wilcoxon rank sum test
The two population distributions are identical in shape and spread
When we have ordinal data, the differences between the numbers are/are not meaningful and the rankings are/are not essential
When we have ordinal data, the differences between the numbers are not meaningful and the rankings are essential
Wilcoxon Rank Sum Test and Wilcoxon Rank sum signed test have same nulls and...
alternatives
Why do we choose the number of positive differences as our test statistic for sign test
arbitrary
Sign test is valid for both ranked and quantitative non normal matched pairs data. Why don't we use is for quantitative non normal matched pairs data. what test do we use instead?
because we have more powerful tests for this data such as wilcoxon rank sum signed test
What is the distribution of sign test statistic under the null. with p equal what?
distributed as a binomial random variable with p = 0.5
Sign test- when the number of zero differences is n and H0 is true, the expected number of positive differences is?
n * 0.5
Do non parametric techniques involve testing a particular parameter of the distribution such as the mean?
no
Since with ordinal data, the assigned numbers are unimportant, are means and variances useful
no
do non parametric techniques rely on any assumed distribution for the data?
no they are distribution free
What is the number of observations in the sign test
number of differences between observations excluding zero differences
As well as ordinal data, non parametric techniques can be used for
quantative data that fail normality requirement
If the ranks of the data in the sample taken from population 1 are higher than the ranks in the second sample from population, we can conclude that the location of population 1 lies to the ..... of population 2
right
The mean of the distribution for T (wilcoxon rank sum test), rises when what rises?
sample size
Distribution of T (wilcoxon rank sum test statistic) approximates a normal distribution, when we have how many observations?
sample size greater than 10
What specifically makes sign test not powerful for quantitative non normal matched pairs data. (refer to the differences) How does wilcoxon rank sum sign test fix this?
the size of the differences between quantativative variables is important. Therefore in Wilcoxon Ranked Sum Signed Test we take the differences between observations and then rank them
What is the test statistic a value of in sign test
the total number of positive differences
Which rank sum do we choose as our test statistic
we arbritarily choose the first rank sum
