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 #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 ***
---
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 #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
---
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.