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A p-value, or probability value, is a number describing how likely it is that your data would have occurred by random chance (i.e. that the null hypothesis is true). It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random).

It will be the case that if you observed a sample that’s impossible under the null (and if the statistic is able to detect that), you can get a p-value of exactly zero.

The p-value is a measure of how much evidence we have against the null hypothesis. A p-value less than 0.01 will under normal circumstances mean that there is substantial evidence against the null hypothesis.

Conventionally the 5% (less than 1 in 20 chance of being wrong), 1% and 0.1% (P < 0.05, 0.01 and 0.001) levels have been used. Most authors refer to statistically significant as P < 0.05 and statistically highly significant as P < 0.001 (less than one in a thousand chance of being wrong).

The tables (or Excel) will tell you, for example, that if there are 100 pairs of data whose correlation coefficient is 0.254, then the p-value is 0.01. This means that there is a 1 in 100 chance that we would have seen these observations if the variables were unrelated.

null hypothesis

If there is less than a 5% chance of a result as extreme as the sample result if the null hypothesis were true, then the null hypothesis is rejected. When this happens, the result is said to be statistically significant .

NoIntrinsicValue: Significance level when listed in regression results is referring to the p-value (i.e. the lowest level of significance that the null hypothesis can be rejected). In other words, a significance of 0 means there is no level of confidence too high (95%, 99%, etc.)

If the computed t-score equals or exceeds the value of t indicated in the table, then the researcher can conclude that there is a statistically significant probability that the relationship between the two variables exists and is not due to chance, and reject the null hypothesis.

The t-value measures the size of the difference relative to the variation in your sample data. Put another way, T is simply the calculated difference represented in units of standard error. The greater the magnitude of T, the greater the evidence against the null hypothesis.

100

Null hypothesis are never accepted. We either reject them or fail to reject them. The distinction between “acceptance” and “failure to reject” is best understood in terms of confidence intervals. Failing to reject a hypothesis means a confidence interval contains a value of “no difference”.

Support or reject null hypothesis? If the P-value is less, reject the null hypothesis. If the P-value is more, keep the null hypothesis. 0.003 < 0.05, so we have enough evidence to reject the null hypothesis and accept the claim.

After you perform a hypothesis test, there are only two possible outcomes.

1. When your p-value is less than or equal to your significance level, you reject the null hypothesis. The data favors the alternative hypothesis.
2. When your p-value is greater than your significance level, you fail to reject the null hypothesis.