What does the P value mean in a two proportion test? (2023)

FAQs

What does the P value mean in a two proportion test? ›

The P-value is the probability of observing a sample statistic as extreme as the test statistic. Since the test statistic is a z-score, use the Normal Distribution Calculator to assess the probability associated with the z-score. (See sample problems at the end of this lesson for examples of how this is done.)

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.

The P-Value Approach

For a population proportion test, the test statistic is a Z-Value from a standard normal distribution. Because this is a two-tailed test, we need to find the P-value of a Z-value smaller than -8 and multiply it by 2.

The P value is defined as the probability under the assumption of no effect or no difference (null hypothesis), of obtaining a result equal to or more extreme than what was actually observed. The P stands for probability and measures how likely it is that any observed difference between groups is due to chance.

A two-proportion Z-test is a statistical hypothesis test used to determine whether two proportions are different from each other. While performing the test, Z-statistics is computed from two independent samples and the null hypothesis is that the two proportions are equal.

P > 0.05 is the probability that the null hypothesis is true. 1 minus the P value is the probability that the alternative hypothesis is true. A statistically significant test result (P ≤ 0.05) means that the test hypothesis is false or should be rejected. A P value greater than 0.05 means that no effect was observed.

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.

Note that the P-value for a two-tailed test is always two times the P-value for either of the one-tailed tests. The P-value, 0.0254, tells us it is "unlikely" that we would observe such an extreme test statistic t* in the direction of H_A if the null hypothesis were true.

If the p-value is less than or equal to the specified significance level α, the null hypothesis is rejected; otherwise, the null hypothesis is not rejected.

If this is a two tailed test and the result is less than 0.5, then the double this number to get the P-Value. If this is a two tailed test and the result is greater than 0.5 then first subtract from 1 and then double the result to get the P-Value.

What does p mean in test statistic? ›

The P value, or calculated probability, is the probability of finding the observed, or more extreme, results when the null hypothesis (H ₀) of a study question is true – the definition of 'extreme' depends on how the hypothesis is being tested.

The Chi-square test is used when comparing the difference in population proportions between 2 or more groups or when comparing a group with a value. The Fisher-exact test is used when comparing the difference in population proportions of 2 very small groups.

Interpretation. Use the p-value to determine whether the population proportion is statistically different from the hypothesized proportion. To determine whether the difference between the population proportion and the hypothesized proportion is statistically significant, compare the p-value to the significance level.

In accordance with the conventional acceptance of statistical significance at a P-value of 0.05 or 5%, CI are frequently calculated at a confidence level of 95%. In general, if an observed result is statistically significant at a P-value of 0.05, then the null hypothesis should not fall within the 95% CI.

For example, a p-value that is more than 0.05 is considered statistically significant while a figure that is less than 0.01 is viewed as highly statistically significant.

eg the p-value = 0.01, it means if you reproduced the experiment (with the same conditions) 100 times, and assuming the null hypothesis is true, you would see the results only 1 time. OR in the case that the null hypothesis is true, there's only a 1% chance of seeing the results.

Therefore, P values only indicate how incompatible the data are with a specific statistical model (usually with a null-hypothesis). The smaller the P value, the greater statistical incompatibility of the data with the null hypothesis.

The p-value can be perceived as an oracle that judges our results. If the p-value is 0.05 or lower, the result is trumpeted as significant, but if it is higher than 0.05, the result is non-significant and tends to be passed over in silence.

The p-value of 0.15, means that the observed difference can be attributed to chance by 15%. In Fisher's approach the null hypothesis is never proved, but is possibly disproved.

What is the p-value in lower tailed test? ›

For a lower-tail test, the p-value is the area under the curve of the t-distribution (with n−1 degrees of freedom) to the left of the observed t-statistic.

If a p-value reported from a t test is less than 0.05, then that result is said to be statistically significant. If a p-value is greater than 0.05, then the result is insignificant.

In a two-tailed test the decision rule has investigators reject H₀ if the test statistic is extreme, either larger than an upper critical value or smaller than a lower critical value. The exact form of the test statistic is also important in determining the decision rule.

The one-tail P value is half the two-tail P value. The two-tail P value is twice the one-tail P value (assuming you correctly predicted the direction of the difference). This rule works perfectly for almost all statistical tests.

If the p-value is greater than alpha, you accept the null hypothesis. If it is less than alpha, you reject the null hypothesis.

Broadly, a p-value can be described as the probability that a certain statistical value would be equal to or more extreme than its observed value.

It produces a “p-value”, which can be used to decide whether there is evidence of a difference between the two population means. The p-value is the probability that the difference between the sample means is at least as large as what has been observed, under the assumption that the population means are equal.

In order to determine if two numbers are significantly different, a statistical test must be conducted to provide evidence. Researchers cannot rely on subjective interpretations. Researchers must collect statistical evidence to make a claim, and this is done by conducting a test of statistical significance.

The point estimate for the difference between the two population proportions, p 1 − p 2 , is the difference between the two sample proportions written as p ^ 1 − p ^ 2 .

A proportion is a part, share or number considered in comparative relation to a whole. It can be equal to 0, 1 or any value between 0 and 1. It can be expressed as a number or percentage. One example in official statistics would be the proportion of the Canadian population who lives in a given province.

How do you find the proportion of p-value? ›

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.

The standard error of a sample proportion can be calculated as: Standard error = √p(1-p) / n. where: p is the proportion of successes. n is the sample size.

A p-value is a probability, a number between 0 and 1, calculated after running a statistical test on data. A small p-value (< 0.05 in general) means that the observed results are so unusual assuming that they were due to chance only.

P-values are expressed as decimals and can be converted into percentage. For example, a p-value of 0.0237 is 2.37%, which means there's a 2.37% chance of your results being random or having happened by chance. The smaller the P-value, the more significant your results are.

The test statistic is a z-score (z) defined by the following equation. z=(p−P)σ where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and σ is the standard deviation of the sampling distribution.

If the p-value is very high (e.g., 0.99), then your observations are well within the bounds of what we would expect if the null hypothesis were true. That is, your data doesn't support a rejection of the null hypothesis.

If the p-value is less than 0.05, we reject the null hypothesis that there's no difference between the means and conclude that a significant difference does exist. If the p-value is larger than 0.05, we cannot conclude that a significant difference exists. That's pretty straightforward, right? Below 0.05, significant.

the value will usually range between 0 and 1. Value of < 0.3 is weak , Value between 0.3 and 0.5 is moderate and Value > 0.7 means strong effect on the dependent variable.

What does p-value mean error? ›

Type I error

That's a value that you set at the beginning of your study to assess the statistical probability of obtaining your results (p value). The significance level is usually set at 0.05 or 5%. This means that your results only have a 5% chance of occurring, or less, if the null hypothesis is actually true.

Standard Error = √p̂(1-p̂) / n

What is this? We then typically use this standard error to calculate a confidence interval for the true proportion of residents who support the law.

The p value, or probability value, tells you how likely it is that your data could have occurred under the null hypothesis. It does this by calculating the likelihood of your test statistic, which is the number calculated by a statistical test using your data.