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Here is my model and output:

plants_lm <- lm(weight ~ group, data = plants)

summary(plants_lm)

Call:
lm(formula = weight ~ group, data = plants)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.0710 -0.4180 -0.0060  0.2627  1.3690 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)        5.0320     0.1971  25.527   <2e-16 ***
groupFertlizer_A  -0.3710     0.2788  -1.331   0.1944    
groupFertlizer_B   0.4940     0.2788   1.772   0.0877 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6234 on 27 degrees of freedom
Multiple R-squared:  0.2641,    Adjusted R-squared:  0.2096 
F-statistic: 4.846 on 2 and 27 DF,  p-value: 0.01591

I don't understand how the predictors (levels of "group") are both insignificant, yet the model is somehow significant. I found this post: Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?

But none of this seems to apply here. The answers on that post say it can happen if the predictors are correlated (in my case they can't be, they are separate treatments) or if two or more predictors are close to significant. That doesn't seem to be the case here as Fertilizer A is not close. Or is it? What is "close"? Any insight appreciated.

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  • $\begingroup$ Remember what the tests on the individual coefficients are testing as opposed to the overall test. If that does not help try changing the reference category and refit the model. $\endgroup$
    – mdewey
    Commented Oct 5, 2021 at 14:17
  • $\begingroup$ But my reference is the control. Surely I want that to be the reference? $\endgroup$
    – Elasso
    Commented Oct 5, 2021 at 14:18
  • $\begingroup$ And can you elaborate on your statement? Sorry, I am a stats beginner and trying to learn R at the same time and it's a bit overwhelming. What is it that the individual coefficients are testing compared to the overall test? If I am trying to determine if Fertilizer A or B have an impact on plant growth rates, which is more important? $\endgroup$
    – Elasso
    Commented Oct 5, 2021 at 14:19
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    $\begingroup$ Similar questions: stats.stackexchange.com/questions/155459/…, stats.stackexchange.com/questions/94441/… (see answer by @gung:), stats.stackexchange.com/questions/549815/… and many more ... $\endgroup$
    – kjetil b halvorsen ♦
    Commented Nov 11, 2021 at 11:57
  • 1
    $\begingroup$ To the original question, lots of small "insignificant" effects can add up to a bigger effect. $\endgroup$
    – Frank Harrell
    Commented Nov 11, 2021 at 12:49

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