How do I calculate SS of a Variable and Error provided data
Multi tool use
$begingroup$
Yields are noted for tree samples from four different varieties in crops in Argentina.
The following varieties are:
Variety A = 15, 14, 12, 13
Variety B = 11, 18, 13
Variety C = 18, 25, 19, 20
Variety D = 19, 20, 24.
My "teacher" gave me the values of:
SS Variety = 172.36
SS Error = 74
I am competent with calculating degrees of freedom. But here, he provided me with these values, I would like to ask how they calculated.
My knowledge with ANOVA is that SS = Sum of Squares. With other examples I would square each data value - but I would think that it would clearly exceed the value given.
And so I am asking - how this value is calculated.
Thanks.
statistics statistical-inference
asked Jan 8 at 22:22
princetongirl818princetongirl818
948
$endgroup$
add a comment |
$begingroup$
Yields are noted for tree samples from four different varieties in crops in Argentina.
The following varieties are:
Variety A = 15, 14, 12, 13
Variety B = 11, 18, 13
Variety C = 18, 25, 19, 20
Variety D = 19, 20, 24.
My "teacher" gave me the values of:
SS Variety = 172.36
SS Error = 74
I am competent with calculating degrees of freedom. But here, he provided me with these values, I would like to ask how they calculated.
My knowledge with ANOVA is that SS = Sum of Squares. With other examples I would square each data value - but I would think that it would clearly exceed the value given.
And so I am asking - how this value is calculated.
Thanks.
statistics statistical-inference
asked Jan 8 at 22:22
princetongirl818princetongirl818
948
$endgroup$
add a comment |
$begingroup$
Yields are noted for tree samples from four different varieties in crops in Argentina.
The following varieties are:
Variety A = 15, 14, 12, 13
Variety B = 11, 18, 13
Variety C = 18, 25, 19, 20
Variety D = 19, 20, 24.
My "teacher" gave me the values of:
SS Variety = 172.36
SS Error = 74
I am competent with calculating degrees of freedom. But here, he provided me with these values, I would like to ask how they calculated.
My knowledge with ANOVA is that SS = Sum of Squares. With other examples I would square each data value - but I would think that it would clearly exceed the value given.
And so I am asking - how this value is calculated.
Thanks.
statistics statistical-inference
asked Jan 8 at 22:22
princetongirl818princetongirl818
948
$endgroup$
Yields are noted for tree samples from four different varieties in crops in Argentina.
The following varieties are:
Variety A = 15, 14, 12, 13
Variety B = 11, 18, 13
Variety C = 18, 25, 19, 20
Variety D = 19, 20, 24.
My "teacher" gave me the values of:
SS Variety = 172.36
SS Error = 74
I am competent with calculating degrees of freedom. But here, he provided me with these values, I would like to ask how they calculated.
My knowledge with ANOVA is that SS = Sum of Squares. With other examples I would square each data value - but I would think that it would clearly exceed the value given.
And so I am asking - how this value is calculated.
Thanks.
statistics statistical-inference
statistics statistical-inference
asked Jan 8 at 22:22
princetongirl818princetongirl818
948
asked Jan 8 at 22:22
princetongirl818princetongirl818
948
edited Jan 8 at 22:55
princetongirl818
asked Jan 8 at 22:22
princetongirl818princetongirl818
948
asked Jan 8 at 22:22
princetongirl818princetongirl818
948
asked Jan 8 at 22:22
princetongirl818princetongirl818
948
948
add a comment |
add a comment |
1 Answer
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$begingroup$
The overall mean is about $17.21429$ while the means for each variety are $13.5,14,20.5,21$
What you are describing as SS Variety is calculated as $$4times (13.5-17.21429)^2 + 3times (14-17.21429)^2 + 4times (20.5-17.21429)^2 + 3times (21.5-17.21429)^2$$
What you are describing as SS Error is calculated as $$(15-13.5)^2 + (14-13.5)^2 + (12-13.5)^2 + (13-13.5)^2 + \ (11-14)^2 + (13-14)^2 + (18-14)^2 + \ (18-20.5)^2 + (25-20.5)^2 + (19-20.5)^2 + (20-20.5)^2 + \ (19-21)^2 + (20-21)^2 + (24-21)^2 $$
If you add these together, you get the overall sum of squares of differences from the overall mean of about $246.3571$
answered Jan 9 at 1:11
HenryHenry
100k481167
$endgroup$
$begingroup$
Thank you a lot for your help. This made things a lot clearer.
$endgroup$
– princetongirl818
Jan 10 at 22:29
add a comment |
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1 Answer
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$begingroup$
The overall mean is about $17.21429$ while the means for each variety are $13.5,14,20.5,21$
What you are describing as SS Variety is calculated as $$4times (13.5-17.21429)^2 + 3times (14-17.21429)^2 + 4times (20.5-17.21429)^2 + 3times (21.5-17.21429)^2$$
What you are describing as SS Error is calculated as $$(15-13.5)^2 + (14-13.5)^2 + (12-13.5)^2 + (13-13.5)^2 + \ (11-14)^2 + (13-14)^2 + (18-14)^2 + \ (18-20.5)^2 + (25-20.5)^2 + (19-20.5)^2 + (20-20.5)^2 + \ (19-21)^2 + (20-21)^2 + (24-21)^2 $$
If you add these together, you get the overall sum of squares of differences from the overall mean of about $246.3571$
answered Jan 9 at 1:11
HenryHenry
100k481167
$endgroup$
$begingroup$
Thank you a lot for your help. This made things a lot clearer.
$endgroup$
– princetongirl818
Jan 10 at 22:29
add a comment |
$begingroup$
The overall mean is about $17.21429$ while the means for each variety are $13.5,14,20.5,21$
What you are describing as SS Variety is calculated as $$4times (13.5-17.21429)^2 + 3times (14-17.21429)^2 + 4times (20.5-17.21429)^2 + 3times (21.5-17.21429)^2$$
What you are describing as SS Error is calculated as $$(15-13.5)^2 + (14-13.5)^2 + (12-13.5)^2 + (13-13.5)^2 + \ (11-14)^2 + (13-14)^2 + (18-14)^2 + \ (18-20.5)^2 + (25-20.5)^2 + (19-20.5)^2 + (20-20.5)^2 + \ (19-21)^2 + (20-21)^2 + (24-21)^2 $$
If you add these together, you get the overall sum of squares of differences from the overall mean of about $246.3571$
answered Jan 9 at 1:11
HenryHenry
100k481167
$endgroup$
$begingroup$
Thank you a lot for your help. This made things a lot clearer.
$endgroup$
– princetongirl818
Jan 10 at 22:29
add a comment |
$begingroup$
The overall mean is about $17.21429$ while the means for each variety are $13.5,14,20.5,21$
What you are describing as SS Variety is calculated as $$4times (13.5-17.21429)^2 + 3times (14-17.21429)^2 + 4times (20.5-17.21429)^2 + 3times (21.5-17.21429)^2$$
What you are describing as SS Error is calculated as $$(15-13.5)^2 + (14-13.5)^2 + (12-13.5)^2 + (13-13.5)^2 + \ (11-14)^2 + (13-14)^2 + (18-14)^2 + \ (18-20.5)^2 + (25-20.5)^2 + (19-20.5)^2 + (20-20.5)^2 + \ (19-21)^2 + (20-21)^2 + (24-21)^2 $$
If you add these together, you get the overall sum of squares of differences from the overall mean of about $246.3571$
answered Jan 9 at 1:11
HenryHenry
100k481167
$endgroup$
The overall mean is about $17.21429$ while the means for each variety are $13.5,14,20.5,21$
What you are describing as SS Variety is calculated as $$4times (13.5-17.21429)^2 + 3times (14-17.21429)^2 + 4times (20.5-17.21429)^2 + 3times (21.5-17.21429)^2$$
What you are describing as SS Error is calculated as $$(15-13.5)^2 + (14-13.5)^2 + (12-13.5)^2 + (13-13.5)^2 + \ (11-14)^2 + (13-14)^2 + (18-14)^2 + \ (18-20.5)^2 + (25-20.5)^2 + (19-20.5)^2 + (20-20.5)^2 + \ (19-21)^2 + (20-21)^2 + (24-21)^2 $$
If you add these together, you get the overall sum of squares of differences from the overall mean of about $246.3571$
answered Jan 9 at 1:11
HenryHenry
100k481167
answered Jan 9 at 1:11
HenryHenry
100k481167
answered Jan 9 at 1:11
HenryHenry
100k481167
answered Jan 9 at 1:11
HenryHenry
100k481167
100k481167
$begingroup$
Thank you a lot for your help. This made things a lot clearer.
$endgroup$
– princetongirl818
Jan 10 at 22:29
add a comment |
$begingroup$
Thank you a lot for your help. This made things a lot clearer.
$endgroup$
– princetongirl818
Jan 10 at 22:29
$begingroup$
Thank you a lot for your help. This made things a lot clearer.
$endgroup$
– princetongirl818
Jan 10 at 22:29
$begingroup$
Thank you a lot for your help. This made things a lot clearer.
$endgroup$
– princetongirl818
Jan 10 at 22:29
add a comment |
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