(Am I WRONG or is "STATISTICS WRONG"?)

YATES ANALYSIS (The “usual calculations” SEEM TO BE WRONG!)

These values could be considered as “idealised results” for 3 variables, each at 2 different levels.

For each “result” the variable levels for that particular result is [N;C value;B value;A value]

0 = low; 1 = high

1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111

1001-1000 = effect of changing “A value” from high to low. Etc.

ALSO (for 2 way interaction)

1011-1000 = effect of changing “for 2 way interaction of AB value” from high to low. Etc.

STANDARD YATES ANALYSIS

The MAIN "difference" is measured from the "baseline"

The TWO WAY INTERACTION "difference" IS NOT measured from the "baseline".

(It seems to be measuring a "difference" between 2 "different TWO WAY INTERACTION results values" that have the same "levels" for the variables.)

A "variance ratio" should be comparing "very similar values". IT DOESN'T!

“usual calculations” (which give the same results as for ANOVA)

- give differences, from the “baseline reference value”, for the “MAIN effects”

- give differences, as “self-reference values”, between 2 of “the same interaction results”, for the “INTERACTION effects”.

“Variance ratios”, must, by their very nature (& mathematically) must have considerable similarity. For this"variance ratio", it’s like dividing the number of peas by the length of carrots! Meaningless mathematically! You can’t divide the number of teeth by the “number blue”, to get a ratio!

The “usual calculations”, below, has calculated VERY DIFFERENT (i.e. WRONG!) values for the “Yates Calculation Value” and hence the calculated “Yates effect”.

1cba-------------Yates--calc---------effect

1000---2001---4022---8444---8---1055.5

1001---2021---4422--------4---4--------1

1010---2201--------2-------40---4------10

1011---2221--------2---------0---2--------0

1100--------1--------0------400---4-----100

1101--------1-------20---------0---2--------0

1110--------1---------0---------0---2--------0

1111--------1---------0---------0----1-------0

##################

MODIFIED YATES ANALYSIS

The “MODIFIED calculations”, below, has calculated the values LOGICALLY (i.e. RIGHT!) values for the “Yates Calculation Value” and hence the calculated CORRECT “Yates effect”

The MAIN "difference" is measured from the "baseline"

The TWO WAY INTERACTION "difference" IS measured from the "baseline"

The "variance ratio" can be compared as they are "very similar values" of "the same type".

.(The "variance ratio" for the TWO WAY INTERACTION & the THREE WAY INTERACTION, will be "different" for these calculations, compared to the "usual calculations"!)

1cba-------------Yates--calc---------effect

1000---2001---4022---8444---8---1055.5

1001---2021---4422--------4---4--------1

1010---2201--------2------40---4-------10

1011---2221--------2------22---2--------11

1100--------1------20-----400---4------100

1101--------1------20-----202---2------101

1110--------1--------0-----220---2------110

1111--------1--------0------111---1------111

The "Modification factors":-

[row heading] [calculation for “Yates Calculation Value” ] [“Yates Calculation Value” ]

[1011] # [(1111-1000)+(1100-1011)] # [22]

[1101] # [(1111-1000)+(1101-1010)] # [202]

[1110] # [(1111-1000)+(1110-1001)] # [220]

[1111] # [1111-1000 ] ############ [111]

(This problem of "Yates effects" & "variance ratios" being "illogical", was found when "my simple statistical analysis" {independently derived from first principles} was DIFFERENT from the STANDARD YATES ANALYSIS! The values calculated from MODIFIED YATES ANALYSIS matches "my simple statistical analysis" values! "My simple statistical analysis" (fairly) easily calculates 4 "virtual results" for each of the 8 "experiments", allowing "in-depth statistical analysis"!)

[Formatting is a problem. The formatting seen during EDITING is different to what is seen after SAVE & both are different what is from a "wordprocessor COPY"!]

YATES ANALYSIS (The “usual calculations” SEEM TO BE WRONG!)

These values could be considered as “idealised results” for 3 variables, each at 2 different levels.

For each “result” the variable levels for that particular result is [N;C value;B value;A value]

0 = low; 1 = high

1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111

1001-1000 = effect of changing “A value” from high to low. Etc.

ALSO (for 2 way interaction)

1011-1000 = effect of changing “for 2 way interaction of AB value” from high to low. Etc.

STANDARD YATES ANALYSIS

The MAIN "difference" is measured from the "baseline"

The TWO WAY INTERACTION "difference" IS NOT measured from the "baseline".

(It seems to be measuring a "difference" between 2 "different TWO WAY INTERACTION results values" that have the same "levels" for the variables.)

A "variance ratio" should be comparing "very similar values". IT DOESN'T!

“usual calculations” (which give the same results as for ANOVA)

- give differences, from the “baseline reference value”, for the “MAIN effects”

- give differences, as “self-reference values”, between 2 of “the same interaction results”, for the “INTERACTION effects”.

“Variance ratios”, must, by their very nature (& mathematically) must have considerable similarity. For this"variance ratio", it’s like dividing the number of peas by the length of carrots! Meaningless mathematically! You can’t divide the number of teeth by the “number blue”, to get a ratio!

The “usual calculations”, below, has calculated VERY DIFFERENT (i.e. WRONG!) values for the “Yates Calculation Value” and hence the calculated “Yates effect”.

1cba-------------Yates--calc---------effect

1000---2001---4022---8444---8---1055.5

1001---2021---4422--------4---4--------1

1010---2201--------2-------40---4------10

1011---2221--------2---------0---2--------0

1100--------1--------0------400---4-----100

1101--------1-------20---------0---2--------0

1110--------1---------0---------0---2--------0

1111--------1---------0---------0----1-------0

##################

MODIFIED YATES ANALYSIS

The “MODIFIED calculations”, below, has calculated the values LOGICALLY (i.e. RIGHT!) values for the “Yates Calculation Value” and hence the calculated CORRECT “Yates effect”

The MAIN "difference" is measured from the "baseline"

The TWO WAY INTERACTION "difference" IS measured from the "baseline"

The "variance ratio" can be compared as they are "very similar values" of "the same type".

.(The "variance ratio" for the TWO WAY INTERACTION & the THREE WAY INTERACTION, will be "different" for these calculations, compared to the "usual calculations"!)

1cba-------------Yates--calc---------effect

1000---2001---4022---8444---8---1055.5

1001---2021---4422--------4---4--------1

1010---2201--------2------40---4-------10

1011---2221--------2------22---2--------11

1100--------1------20-----400---4------100

1101--------1------20-----202---2------101

1110--------1--------0-----220---2------110

1111--------1--------0------111---1------111

The "Modification factors":-

[row heading] [calculation for “Yates Calculation Value” ] [“Yates Calculation Value” ]

[1011] # [(1111-1000)+(1100-1011)] # [22]

[1101] # [(1111-1000)+(1101-1010)] # [202]

[1110] # [(1111-1000)+(1110-1001)] # [220]

[1111] # [1111-1000 ] ############ [111]

(This problem of "Yates effects" & "variance ratios" being "illogical", was found when "my simple statistical analysis" {independently derived from first principles} was DIFFERENT from the STANDARD YATES ANALYSIS! The values calculated from MODIFIED YATES ANALYSIS matches "my simple statistical analysis" values! "My simple statistical analysis" (fairly) easily calculates 4 "virtual results" for each of the 8 "experiments", allowing "in-depth statistical analysis"!)

[Formatting is a problem. The formatting seen during EDITING is different to what is seen after SAVE & both are different what is from a "wordprocessor COPY"!]

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