Using Table E.6, determine the lower-tail critical value for the Wilcoxon rank sum test statisti

Using Table E.6, determine the lower-tail critical value for...

Key Concepts

Wilcoxon Rank Sum Test

The Wilcoxon rank sum test is a nonparametric statistical test used to compare two independent samples to assess whether their population distributions differ. It does not assume normality of the data and is particularly useful when data are ordinal or when the assumption of equal variances is questionable.

Test Statistic and Critical Values

In hypothesis testing, the Wilcoxon rank sum test involves calculating a test statistic based on the sum of ranks of one of the samples. Critical values are threshold values obtained from a table (like Table E.6) corresponding to a chosen significance level; they determine the boundaries of the rejection region for the test.

Lower-Tail Test

A lower-tail test focuses on the lower end of the distribution of the test statistic. This means that small values of the test statistic are considered evidence against the null hypothesis. The lower-tail critical value is the value below which the probability of observing a test statistic is equal to the significance level.

Significance Level (?)

The significance level, denoted by ?, represents the probability of rejecting the null hypothesis when it is actually true (Type I error). In the context of the Wilcoxon rank sum test, different ? levels (such as 0.05, 0.025, 0.01, 0.005) determine different critical values, adjusting the strictness of the test’s rejection criteria.

Transcript

00:01 Hi, in this question we're gonna see how to find the critical value so let me explain something here then we're gonna go how to find the critical value from the table so in both cases for the left tailed and right tailed we're gonna call it one tailed okay and for the right tailed okay it's gonna be the value from here and it's always gonna be a positive value and for the left tail that's gonna be the area from here and it will be a negative value so whatever the value of here in the table it's gonna be positive value so we're gonna keep the sign for the right tailed and for the left tail we're gonna take that the same absolute value and put a negative sign in front of it and in case of two tail okay you're gonna get a positive value from the so the negative value is going to be here this area and the positive one is going to be from here and i'm going to show you in seconds how to find these also in microsoft excel so the first one is asking about the degree freedom of 11 because the sample size or n is 12 and alpha is point on one and it's asking about the left tilt so we get that 11 here okay and degree of freedom of 0 .01 for one tail this one and this one so you're gonna go across and you find it 2 .718 and the second one is gonna be 1 .753 because n is 16 and the alpha is 0 .05 and it's asking about the right tailed and the third one is gonna be here because n is 7 alpha is 0 .1 and it is 2 tails so it's gonna be 1 in that case 1 .9 4 3 and he minus 1 .9 for 3 and the 4th 1 .1 is here and the 4th one is here because n is 11 so the degree of freedom is 10 and it's asking about 0 .025 1 tail the right one so going to be a positive value of 2 .228 and the last one is about two -tailed so it's asking about alpha is 0 .05 and n is 10 which is equivalently to degree of freedom of 9 and it's going to be also two values the positive one is going to be the upper one or 2 .262 and the lower 1 is minus 2 .262 and as you can see here it's matching that values that i compute from microsoft excel.

03:12 And here's the function you are using.

03:15 So if it is one tail, you're going to use t.

03:19 .

03:19 Then you just put the c3, which is here...

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