Tham khảo tài liệu 'data analysis and presentation skills part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 140 5 STATISTICAL ANALYSIS Least significant difference LSD analysis Using this test we are able to compare all of the differences between mean values in our data set and determine what the lowest value for the difference between any pair of means would need to be for there to be significance at a given level. The steps in the calculation of the LSD may be seen below. Multiple range test - least significant difference between means test 1. The first step is to calculate the standard error of the difference between any two group means from the formula . p mean square within groups 1 n 1 n Equation where the mean square MS within groups has been calculated in the analysis of variance and is shown in the ANOVA table under Sources of Variation Within Groups and n is the number of observations in each group. So for our example from the ANOVA table the mean square within samples groups and n 5 therefore . P 1 5 1 5 so this would be calculated in Excel from the formula SQRT 1 5 1 5 Having entered the formula into an active cell the value of should be returned. 2. We now use the . to find what the least difference between means will be for various levels of significance. From the ANOVA table the degrees of freedom df associated with the mean square within groups is 19 calculated on the basis that there were five observations in each group and four treatments so df 5 X 4 1 . ANALYSIS OF VARIANCE 141 Using the table of critical values for the Student t-test in the Appendix look up the 5 per cent and 1 per cent points of the t-distribution for 19 should find that these are and respectively. The LSD is calculated by multiplying the . by each value therefore the smallest difference between means at the 5 per cent level will be X and at the 1per cent level will be X . In order to find out where significant differences are we must take each set of means for each pH and subtract differences.
