The following data were generated from a blocked experiment. Conduct a Friedman test to determin

The following data were generated from a blocked experiment....

Key Concepts

Null Hypothesis in the Friedman Test

In a Friedman test, the null hypothesis typically posits that there are no differences in the median responses across the treatment groups. This implies that any variations observed in the ranking of the data are due to random chance rather than systematic treatment effects.

Non-parametric Methods

Non-parametric methods are statistical techniques that do not rely on data belonging to any particular distribution, such as the normal distribution. These methods are particularly useful when the data do not meet the conditions required for parametric tests, making them versatile tools in the analysis of experimental data.

Chi-Square Distribution

The chi-square distribution is used to approximate the distribution of the Friedman test statistic. Under the null hypothesis, with a sufficient number of blocks, the computed test statistic follows a chi-square distribution with degrees of freedom equal to the number of treatments minus one, which is essential for determining the significance of the results.

Blocked Experimental Design

A blocked experimental design is a method used to reduce variability in experimental data by grouping similar subjects or units together into blocks. By doing so, any differences within these groups can be controlled, ensuring that variability is minimized and the effects of treatments can be more accurately assessed.

Friedman Test

The Friedman test is a non-parametric statistical test used to evaluate differences across multiple treatments in a blocked or repeated-measures design. It ranks the data within each block and then tests for significant differences among the ranks across treatments, serving as an alternative to the parametric repeated measures ANOVA when its assumptions are not met.

Transcript

00:01 Hello show and we are given assume that the population are normally distributed right population are normally distributed test where mu1 is greater than equals to mu 2 at alpha equals to 0 .05 level of significance for sample data right so we can write for population one and population two we can write the things here so sample size is 33 here and here turn here is 13 and a mean of population sorry, mean of sample data is 43 .1 here and here in the second case, this is 41 .0, right? now, in the third case, if i write, s1 would be 4 .5 and s2 would be 5 .1.

00:53 Now, let us calculate together.

00:57 Now, if i write for the a term, right, so basically, mu1 and mu2 are population mean.

01:08 Right now if i write here so we need to we need to test whether whether mu one is greater than mu two or not right at at alpha equals to 0 .05 significance level significance level right now if i write for this so h not represent null hypothesis where mu1 is greater than mu 2 and h1 is mu 1 is not equal to mu 2 having possibility this is or this is right so let us calculate our t statics right so what is our the test statistics are statistics are so here t0 value would be calculated as x 1 bar minus x2 bar x1 bar minus x2 bar minus mu 2 divided by so basically we are assuming null hypothesis in the first so this is n1 n plus s2 squared divided by n2 right so basically this is x1 bar minus x2 bar right now if i write for this so this is 43 .1 minus 41 43 .1 minus 41 and this is under root of s 1 square as 1 square is basically 4 .5 square divided by n1 right divided by n1 and n1 is basically 23 plus if i write for this s2 square would be 5 .1 square divided by each so basically this is 13 right now if i write for this we can write this is 43 .1 minus 41 2 .1 under root so no but we need to calculate something like this so this is the 2 .1 but divided by 4 .5 multiply by 4 .5 20 .25 divided by 23 which is 0 .88 again 0 .88 right 0 .04 plus 5 .1 multiply by 5 .1 26 .01 divided by 13 so this can be written as 2 right this can be written as 2.

04:13 Now 2 .1 divided by under root 2 .88 so basically this can be written as 2 .1 divided by under root 2 .88 so basically this is 1 .2 and this is round root of round root of 4 right so basically t not is 1 .24 here now we need to understand one thing right so we need to understand our p value what is p value p value is basically the value here these area this area is referred as p values right having 0 .05 significance level alpha equals to 0 .05 right so basically this is the t distribution curve having these is considered area so this is minus 1 .414 1 .24 and plus 1 .24 right so basically if i write for this, p value would be for tf right df 1 is our df is basically degree of freedom in the first case so degree of freedom in the first case is n minus 1 which is 22 right so p value would be for this to multiply by t0 t0 is greater than this is 1 .24 now so t0 is than if i write here p t not is greater than 1 .24 symmetric so multiplied by 2 right so value would be to multiply by 0 .114 can be written as 0 .228 right so basically here what we are seeing this p value is greater than alpha p value is greater than alpha right so we can write point point 0 .228 is greater than.

06:19 So this is the first case is greater than 0 .05...

Please give Ace some feedback