The P Value As A Measure Of The Evidence Against The Null...

The p-value is a measure of the strength of the evidence against the null hypothesis. The p-value is the probability of getting the observed value of the test statistic, or a value with the even greater evidence against Ho, if the null hypothesis is actually true. The smaller the p-value, the greater the evidence against the null hypothesis. If we have a given significance level, then we reject. If we do not have a given significance level, then it is not as cut-and-dried. If the P-value is less than (or equal to) ÃŽ ±, then the null hypothesis is rejected in favor of the alternative hypothesis. And, if the P-value is greater than ÃŽ ±, then the null hypothesis is not rejected. All statistical tests produce a p-value and this is equal to the probability of obtaining the observed difference, or one more extreme, if the null hypothesis is true. To put it another way if the null hypothesis is true, the p- value is the probability of obtaining a difference at least as large as that obser ved due to sampling variation. Consequently, if the p-value is small the data support the alternative hypothesis. If the p-value is large the data support the null hypothesis. But how small is ‘small’ and how large is large ‘?! Conventionally a p-value of 0.05 is generally regarded as sufficiently small to reject the null hypothesis. If the p-value is larger than 0.05 we fail to reject the null hypothesis. The 5% value is called the significance level of the test. Other significance levels that areShow MoreRelatedThe T-Distribution and T-Test1259 Words   |  6 Pagesnormally distributed population in situations where the sample size is small† (Narasimhan , 1996). Similar to the normal distribution, the t-distribution is symmetric and bell-shaped, but has heavier tails, meaning that it is more likely to produce values far from its mean. 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