How do I Interpret Significance Codes in R?

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When you perform regression analysis or ANOVA in R, the output tables will contain p-values for the variables used in the analysis along with corresponding significance codes.

These significance codes are displayed as a series of stars or a decimal point if the variables are statistically significant.

Here is how to interpret the various significance codes:

significance code         p-value
   ***                 [0, 0.001]
    **              (0.001, 0.01]
     *               (0.01, 0.05]
     .                (0.05, 0.1]
                         (0.1, 1] 

The following examples show how to interpret these significance codes in practice.

Example: Significance Codes in Regression

The following code shows how to fit a multiple linear regression model with the built-in mtcars dataset using hp, drat, and wt as predictor variables and mpg as the response variable:

#fit regression model using hp, drat, and wt as predictors
model <- lm(mpg ~ hp + drat + wt, data = mtcars)

#view model summary
summary(model)

Call:
lm(formula = mpg ~ hp + drat + wt, data = mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.3598 -1.8374 -0.5099  0.9681  5.7078 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 29.394934   6.156303   4.775 5.13e-05 ***
hp          -0.032230   0.008925  -3.611 0.001178 ** 
drat         1.615049   1.226983   1.316 0.198755    
wt          -3.227954   0.796398  -4.053 0.000364 ***
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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.561 on 28 degrees of freedom
Multiple R-squared:  0.8369,	Adjusted R-squared:  0.8194 
F-statistic: 47.88 on 3 and 28 DF,  p-value: 3.768e-11

Here is how to interpret the significance codes for the three predictor variables:

• hp has a p-value of .001178. Since this value is in the range (0.001, 0.01], it has a significance code of **
• drat has a p-value of .198755. Since this value is in the range (0.1, 1], it has no significance code.
• wt has a p-value of .000364. Since this value is in the range [0, 0.001], it has a significance code of ***

If we used an alpha level of α = .05 to determine which predictors were significant in this regression model, we’d say that hp and wt are statistically significant predictors while drat is not.

Example: Significance Codes in ANOVA

The following code shows how to fit a one-way ANOVA model with the built-in mtcars dataset using gear as the factor variable and mpg as the response variable:

#fit one-way ANOVA
model <- aov(mpg ~ gear, data = mtcars)

#view the model output
summary(model)

            Df Sum Sq Mean Sq F value Pr(>F)   
gear         1  259.7  259.75   8.995 0.0054 **
Residuals   30  866.3   28.88                  
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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Here is how to interpret the significance code in the output:

• gear has a p-value of .0054. Since this value is in the range (0.001, 0.01], it has a significance code of **

Using an alpha level of α = .05, we would say that gear is statistically significant. In other words, there is a statistically significant difference between the mean mpg of cars based on their value for gear.