one sided interpretation and table notation

[David Planiol Sierra]

Hi,

Possibly quite a simple question:

Let's assume I want to compare the GPA of three groups using an OLS. Please note, this is a simplified example, the real data has multiple control variables.
A priori, I hypothesized the following:
H1: GPA(Group B) is different from GPA(Group A)
H2: GPA(Group B) is higher than GPA(Group A)

gpa	Coef.	P>|t|
Class B	0,600	0,080
Class C	0,700	0,090
cons	2,200

I use an alpha of 0.05. Testing for H1 should be two sided, so I do not find support for H1 as 0.080>0.05. Testing for H2 is one sided, so I do find support for H2 as 0.045>0.05 (here I divided 0.090 by 2 as it is one sided).

First question: is my reasoning above correct?

Second question: if I would notate this in a paper with . * p<0.1, ** p<0.05, *** p<0.001 , would I notate it like this:

gpa	Coef.
Class B	0,600*
Class C	0,700**
cons	2,200

Or like this:

gpa	Coef.
Class B	0,600*
Class C	0,700*
cons	2,200

Again, this is a simplified example, I am aware that other tests could have been used.
THank you in advance for your help!

[Carlo Lazzaro]

David:
1) as two-sided p-value is 0.08, other things being equal, at an arbitrary 0.05 yardstick you cannot reject the null that the GPA score totaled on average by A and B does not differ;
2) as far as your second one-sided test is concerned, I'm not clear if you want to compare A vs. B or vs.C. That said, see https://stats.idre.ucla.edu/other/mu...tailed-tests/;
3) the first thing that you should specify as a footnote in your table is what tests are two-sided and one-sided. Significance notation will follow.

[Leonardo Guizzetti]

Carlo has provided some good advice and further reading. I will add a few remarks.

Hi,
H1: GPA(Group B) is different from GPA(Group A)
H2: GPA(Group B) is higher than GPA(Group A)

If you really intended to test group B vs in A twice, then this is a mistake and one of them is scientifically interesting for your research, but not both.

Instead, I assumed that you wanted to contrast A, B and C together, probably comparing B vs A and C vs A.

If this is correct, then a better approach is to use a hierarchical testing framework. First you would test the overall association with -group- (where -group- is a categorical variable for groups A, B or C) using a two-sided test and a alpha level of 0.05, say. This will test the hypothesis that at least one group is different form the others, but does not tell you which contrast is different. If this test meets your criterion for statistically significant, then you can proceed to example pair-wise differences, say B vs A and C vs A as two different two-sided tests.

[David Planiol Sierra]

Hi guys,

Thank you for your help!

Indeed I made a typo, I intended to say:

H1: GPA(Group B) is different from GPA(Group A)
H2: GPA(Group C) is higher than GPA(Group A)

In my research, A receives no treatment and B and C receive a treatment, hence I compare B to A and C to A, and I am not interested in B vs C.

Does your advice above then still hold?

[Leonardo Guizzetti]

Yes.