In tests comparing groups, the p-value is influenced by the difference between the means (or proportions), but also by the variance of the data and by the dimensions of the sample.
Size of sample. The larger the sample the more likely a difference to be detected. Further, a 7 kg difference in a study with 500 participants will give a lower P value than 7 kg difference observed in a study involving 250 participants in each group.
High p-values indicate that your evidence is not strong enough to suggest an effect exists in the population. An effect might exist but it's possible that the effect size is too small, the sample size is too small, or there is too much variability for the hypothesis test to detect it.
The calculation of the p value depends on the statistical test you are using to test your hypothesis: Different statistical tests have different assumptions and generate different test statistics. You should choose the statistical test that best fits your data and matches the effect or relationship you want to test.
Statistical Significance, the Null Hypothesis and P-Values Defined & Explained in One Minute
What determines the p-value?
Mathematically, the p-value is calculated using integral calculus from the area under the probability distribution curve for all values of statistics that are at least as far from the reference value as the observed value is, relative to the total area under the probability distribution curve.
The lower the p-value is, the lower the probability of getting that result if the null hypothesis were true. A result is said to be statistically significant if it allows us to reject the null hypothesis. All other things being equal, smaller p-values are taken as stronger evidence against the null hypothesis.
While a P value can inform the reader whether an effect exists, the P value will not reveal the size of the effect. In reporting and interpreting studies, both the substantive significance (effect size) and statistical significance (P value) are essential results to be reported.
The smaller the p-value the greater the discrepancy: “If p is between 0.1 and 0.9, there is certainly no reason to suspect the hypothesis tested, but if it is below 0.02, it strongly indicates that the hypothesis fails to account for the entire facts. We should not be off- track if we draw a conventional line at 0.05”.
In general, a larger sample size will reduce the probability of a Type I error and therefore decrease the P-value. This raises the possibility that a clinically insignificant difference may be found to be statistically significant.
The p-value is telling you to what degree the results you see are due to randomness. So a low value indicates the results are unlikely due to chance and instead represent actual differences in your data.
If the p-value is greater than the significance level, the decision is to fail to reject the null hypothesis. You do not have enough evidence to conclude that the difference between the population means is statistically significant.
In summary, the p-values of your independent variables can change due to multicollinearity, model specification, changes in degrees of freedom, and alterations in coefficient estimates.
A P value is NOT an error rate, but alpha IS an error rate. By directly comparing the two values in a hypothesis test, it's easy to think they're both error rates. This misconception leads to the most common misinterpretations of P values.
To accommodate for this, the p-value of each individual test is adjusted upward to ensure that the overall risk or family-wise error rate for all tests remains 0.05. Thus, even if more than one test is done, the risk of finding a difference incorrectly significant continues to be 0.05, or one in twenty [4-7].
Small sample sizes, biased sampling, or multiple testing can influence the interpretation of p-values. Be cautious about generalizing findings beyond the specific population and conditions studied.
Summary Genetics plays a substantial role in determining penis size. However, other factors, such as hormones, the environment, and nutrition, can affect penis size. Other factors, including body type, physical fitness, and underlying medical conditions may affect how the penis appears and a person's perception.
If the p-value is less than 0.05, it is judged as “significant,” and if the p-value is greater than 0.05, it is judged as “not significant.” However, since the significance probability is a value set by the researcher according to the circumstances of each study, it does not necessarily have to be 0.05.
The p-value depends on sample size. So, no matter how tiny is your effect size, with enough sample you will find (almost) always statistical significant results.
The P-value is the probability of seeing a sample proportion at least as extreme as the one observed from the data if the null hypothesis is true. In the previous example, only sample proportions higher than the null proportion were evidence in favor of the alternative hypothesis.
A p-value less than or equal to your significance level (typically ≤ 0.05) is statistically significant. A p-value less than or equal to a predetermined significance level (often 0.05 or 0.01) indicates a statistically significant result, meaning the observed data provide strong evidence against the null hypothesis.
Here's how: Precision and Reliability: A larger sample size provides more reliable and precise estimates of the population, leading to narrower confidence intervals. This increased precision leads to a smaller p-value.
The most obvious way is to increase sample sizes. With a bigger (and perhaps costlier) sample, risks are reduced. If you can accept unchanged risk, an alternative would be to loosen p-value requirements.
What is the impact of large samples on the p-value?
There are many advantages to large samples, but researchers using statistical inference must be aware of the p-value problem associated with them. In very large samples, p-values go quickly to zero, and solely relying on p-values can lead the researcher to claim support for results of no practical significance.
