How do I calculate SS of a Variable and Error provided data
$begingroup$
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
1
active
oldest
votes
$begingroup$
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 |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3066813%2fhow-do-i-calculate-ss-of-a-variable-and-error-provided-data%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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 |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3066813%2fhow-do-i-calculate-ss-of-a-variable-and-error-provided-data%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
