You conducted a study to assess the impact of temperature on skin shedding rate in snakes.

The p-value for your linear regression model lm(data=snake_data, shed_rate~temp_degC) was p = 0.0045.

Assuming model design was properly conducted, and the assumptions for a linear regression were met, which of the following statements is an appropriate interpretation of the presented results?

Question

You conducted a study to assess the impact of temperature on skin shedding rate in snakes.

The p-value for your linear regression model lm(data=snake_data, shed_rate~temp_degC) was p = 0.0045.

Assuming model design was properly conducted, and the assumptions for a linear regression were met, which of the following statements is an appropriate interpretation of the presented results?

BlackTom AI · Accepted Answer

First, let's restate what the question is asking: interpret the p-value from a linear regression analysis where shed_rate is modeled as a function of temperature (shed_rate ~ temp_degC), and the reported p-value is 0.0045. We proceed to evaluate each option in light of standard statistical inference.
Option 1: 'There is a 0.45% chance that snake shed rate is not related to temperature.' This is a common misinterpretation. A p-value of 0.0045 does not give the probability that the null hypothesis is true or that there is no relationship with a given probability. It reflects the probability of observing data as extreme as (or more extreme than) what was observed if the null hypothesis of zero slope is true. It is not the probability of no relation in the population.
Option 2: 'The slope of the association between skin shed rate and temperature is not equal to zero.' This is the precise interpretation of a statistically significant result for the slope in a linear regression when p < alpha (commonly 0.05). It means we reject the null hypothesis that the slope equals zero, implying evidence of an association between temperature and shed rate.
Option 3: 'The null hypothesis has been proven false.' In statistical practice, we rarely use the word 'proven' based on a single p-value. We can say we rejected the null under a chosen significance level, but we do not claim absolute certainty or proof; there is always some chance of Type I error and unaccounted assumptions. Saying it is 'proven' overstates the conclusion.
Option 4: 'There is a strong effect of temperature on skin shed rate.' A small p-value indicates that the relationship is statistically significant, but it does not by itself quantify the strength or practical importance of the effect. Measures like the slope magnitude, confidence intervals, or effect size would be needed to judge strength. A significant p-value does not automatically imply a large or strong effect.
In summary, Option 2 correctly aligns with standard interpretation of a significant p-value for a slope in linear regression, while the other options reflect common misinterpretations or overstatements. The incorrect options either misstate probabilistic meaning, overstate certainty, or conflate significance with practical magnitude.

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