Probabilities are written as numbers between 0 and 1; 0 means there is no chance at all, while 1 means that the event is certain. The sum of all probabilities for an experiment is always 1, because if you conduct and experiment, something is bound to happen! For the coin toss example, 0.125 + 0.375 + 0.375 + 0.125 = 1.

There are two broad categories of probability interpretations which can be called “physical” and “evidential” probabilities. Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms.

In the proposed theory of probabilistic argumentation, the credibility (or the weight) of logical arguments is measured by probabilities. For this, we assume the uncertainty of possible premises for defeasible arguments to be adequately representable by a joint probability function.

P(A) = n(A)/n(S) Where, P(A) is the probability of an event “A” n(A) is the number of favourable outcomes. n(S) is the total number of events in the sample space.

The maximum value of the probability of an event will always be 1.

A low P-value indicates that observed data do not match the null hypothesis, and when the P-value is lower than the specified significance level (usually 5%) the null hypothesis is rejected, and the finding is considered statistically significant. First, the tested hypothesis should be defined before inspecting data.

A p-value tells you the probability of having a result that is equal to or greater than the result you achieved under your specific hypothesis. It is a probability and, as a probability, it ranges from 0-1.0 and cannot exceed one.

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 p-values is affected by the sample size. Larger the sample size, smaller is the p-values. Increasing the sample size will tend to result in a smaller P-value only if the null hypothesis is false.

A small P-value signifies that the evidence in favour of the null hypothesis is weak and that the likelihood of the observed differences due to chance is so small that the null hypothesis is unlikely to be true. For example, a P-value of 0.08, albeit not significant, does not mean ‘nil’.

The Chi-square test that you apply yields a P value of 0.04, a value that is less than 0.05. The interpretation is wrong because a P value, even one that is statistically significant, does not determine truth.

statistically significant

The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 19.58. We use the Chi-Square Distribution Calculator to find P(Χ2 > 19.58) = 0.0001. Interpret results. Since the P-value (0.0001) is less than the significance level (0.05), we cannot accept the null hypothesis.

The Chi-Square test is a statistical procedure used by researchers to examine the differences between categorical variables in the same population. The researchers could then perform a Chi-Square test to validate or provide additional context for these observed frequencies.

Significance Levels. The significance level for a given hypothesis test is a value for which a P-value less than or equal to is considered statistically significant. Typical values for are 0.1, 0.05, and 0.01.

The level of statistical significance is often expressed as the so-called p-value. So, you might get a p-value such as 0.03 (i.e., p = . 03). This means that there is a 3% chance of finding a difference as large as (or larger than) the one in your study given that the null hypothesis is true.