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p Value

In education disciplines, quantitative studies conducted via statistical hypothesis testing often depend on the calculation of a probability value or p value. Statistical hypothesis testing is a procedure of evaluating suppositions, which are assumptions about certain characteristics of a population, using a sample from that population. The goal of testing a statistical hypothesis is to determine whether the sample evidence challenges the study’s null hypothesis (i.e., there is no observed effect) and supports the alternative hypothesis (i.e., there is an observed effect).

The idea of p value arises in conjunction with the α (or significance) level associated with a statistical test. The α level is the threshold probability value that is chosen for the test; it is commonly .05 or .01 (equivalently, 5% or 1%). The p value of the sample test is compared with the chosen α level. A small p value indicates the unlikeliness of obtaining the given result if the null hypothesis was true. Therefore, if the associated p value is less than the α level, the sample data provide evidence for rejecting the null hypothesis for the entire population.

The use of a p value typically involves the following steps:

  • state the null hypothesis (H0) and alternative hypothesis (Ha),
  • set the α level,
  • collect data,
  • compute the test statistic and associated p value from the collected data,
  • compare the p value with the significance level α, and
  • make conclusions as to whether the null hypothesis should be rejected.

To understand statistical inference, it is important to understand how to find, use, and interpret p values in a given context.

Applications

Hypothesis tests (z test, t test, F test, and chi-square test) use p values regardless of the test type. In many fields of social science, including education, p values are commonly used to test statistical hypotheses for inferential statistics. Most researchers use statistical software such as SPSS, SAS, Minitab, Excel, and R, or tools available on many websites, to calculate p values.

A Simplified Example

Suppose the following as an example: An innovative teaching approach has been developed for a college-level elementary statistics course. The efficacy of this teaching approach over the traditional approach is analyzed via data gathered from student examination scores. Traditionally, the mean score is 72 with a standard deviation of 9.6. The goal is to provide evidence that the mean score of the students who learned elementary statistics by the new approach is higher than 72. Taking a study sample of 64 exam scores from students taught with the new teaching approach, a sample mean (μ) of 73.5 is obtained.

Note that the sample mean score of 73.5 is greater than 72 by 1.5. To determine whether the sample provides evidence for claiming that this (seeming) improvement is significant, the following steps can be used:

  • State the hypotheses: First, define a random variable X to be the exam score for a student who learned elementary statistics with the new approach. Then, the null hypothesis states that μ = 72 (the mean exam score for those who learned elementary statistics via the new teaching approach is 72), and the alternative hypothesis states that μ > 72.
  • Set the α level: Choose α = .05. (Note: Choose a different α level. However, once the α value is fixed, it should not be changed after find the p value is obtained.)
  • Compute the test statistic: Consider the sampling distribution of the variable X. The central limit theorem allows the normality of the sampling distribution because the sample size of 64 is greater than 30. In the sampling distribution, the test statistic (z statistic) of 73.5 is:

    73.5−729.6/64=1.25.

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