Однофакторный ранговый и дисперсионный анализ в статистическом пакете STATGRAPHICS, страница 3

constructed in such a way that if two means are the same, their

intervals will overlap 95,0% of the time.  You can display the

intervals graphically by selecting Means Plot from the list of

Graphical Options.  In the Multiple Range Tests, these intervals are

used to determine which means are significantly different from which

others.

Multiple Range Tests for abserv by factor

-------------------------------------------------------------------------------Method: 95,0 percent LSD

factor         Count     Mean              Homogeneous Groups

-------------------------------------------------------------------------------1              15        20,6              X 

4              15        28,0667            X

10             15        33,7333             X

7              15        34,4                X

-------------------------------------------------------------------------------Contrast                                   Difference           +/-  Limits

-------------------------------------------------------------------------------1 - 4                                     *-7,46667             4,23721          

1 - 7                                     *-13,8                4,23721          

1 - 10                                    *-13,1333             4,23721          

4 - 7                                     *-6,33333             4,23721          

4 - 10                                    *-5,66667             4,23721           

7 - 10                                     0,666667             4,23721          

-------------------------------------------------------------------------------* denotes a statistically significant difference.

The StatAdvisor

--------------This table applies a multiple comparison procedure to determine

which means are significantly different from which others.  The bottom

half of the output shows the estimated difference between each pair of

means.  An asterisk has been placed next to 5 pairs, indicating that

these pairs show statistically significant differences at the 95,0%

confidence level.  At the top of the page, 3 homogenous groups are

identified using columns of X's.  Within each column, the levels

containing X's form a group of means within which there are no

statistically significant differences.  The method currently being

used to discriminate among the means is Fisher's least significant

difference (LSD) procedure.  With this method, there is a 5,0% risk of

calling each pair of means significantly different when the actual

difference equals 0. 

Variance Check

Cochran's C test: 0,450011   P-Value = 0,0500445

Bartlett's test: 1,56229   P-Value = 0,0000220176

Hartley's test: 17,0484

Levene's test: 7,21208   P-Value = 0,000354849

The StatAdvisor

--------------The four statistics displayed in this table test the null

hypothesis that the standard deviations of abserv within each of the 4

levels of factor is the same.  Of particular interest are the three

P-values.  Since the smallest of the P-values is less than 0,05, there

is a statistically significant difference amongst the standard

deviations at the 95,0% confidence level.  This violates one of the

important assumptions underlying the analysis of variance and will

invalidate most of the standard statistical tests. 

Kruskal-Wallis Test for abserv by factor

factor              Sample Size         Average Rank

-----------------------------------------------------------1                   15                  10,3333             

4                   15                  29,6667            

7                   15                  41,4333            

10                  15                  40,5667            

-----------------------------------------------------------Test statistic = 31,0727   P-Value = 8,20627E-7

The StatAdvisor

--------------The Kruskal-Wallis test tests the null hypothesis that the medians

of abserv within each of the 4 levels of factor are the same.  The

data from all the levels is first combined and ranked from smallest to

largest.  The average rank is then computed for the data at each

level.  Since the P-value is less than 0,05, there is a statistically

significant difference amongst the medians at the 95,0% confidence

level.  To determine which medians are significantly different from

which others, select Box-and-Whisker Plot from the list of Graphical

Options and select the median notch option.