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While studying ANOVA analysis, I meet an example related to the ANOVA table given in the attached figure

enter image description here

Here,

$Y$ stands for change in hemoglobin (%)

$X_1$ stands for duration of the operation (min)

$X_2$ stands for blood loss (ml)

Based on this ANOVA table, several arguments are made:

  • $X_2$ has a significant linear association with $Y$ with or without including $X_1$.

  • $X_1$ has a significant linear association with $Y$ after adjusting for linear effects of blood loss X2 on both $X_1$ and $Y$.

  • Without adjusting for linear effects of $X_2$, the linear relationship between $Y$ and $X_1$ was not quite significant

I am quite confusing on how to generate these three arguments based on the information of ANOVA table? I think it should have connection with those P-values, but do not know how?

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1 Answer 1

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You wrote:

X2 has a significant linear association with Y with or without including X1

This comes from the two p values in the 2nd table.

X1 has a significant linear association with Y after adjusting for linear effects of blood loss X2 on both X1 and Y

This comes from the 2nd line of the first table. But it's not clear, from the table, that the first part of this statement is correct. What exactly do they mean by "after"? This is not standard output; at least, I've not seen it in any other paper that I can recall, nor as output from R or SAS or SPSS.

Without adjusting for linear effects of X2 , the linear relationship between Y and X1 was not quite significant

This comes from the first line of the first table.

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  • $\begingroup$ I believe the OP was trying to ask how these conclusions "come from" the various lines. Bear in mind that not everyone uses 0.05 as a threshold and that plenty of people are confused about what the comparison to the threshold means (and reverse the interpretation). $\endgroup$
    – whuber
    Commented Dec 13, 2023 at 17:58

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