QM Week 3

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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


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