How to find p value from z and significance level?

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In statistics, the p-value is a measure of the strength of evidence against a null hypothesis. It helps us determine the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. The z-score is a standardized value of a random variable, representing how many standard deviations an observation or data point is from the mean. To calculate the p-value from a z-score and significance level, you can follow the steps described below.

Table of Contents

The Steps to Find P-Value from Z-Score and Significance Level:

  • Identify the z-score you have for a specific test statistic or observation.
  • Establish the significance level (alpha) for your hypothesis test. Common choices are 0.05 or 0.01.
  • Determine the type of test you are conducting (one-tailed or two-tailed).
  • Based on the type of test, divide the significance level by 2 (for a two-tailed test) or leave it as it is.
  • Look up the appropriate critical values from a standard normal distribution table or use statistical software.
  • For a one-tailed test:
  • If the z-score is positive and you are performing an upper-tailed test, use the table or software to find the area to the right of the z-score.
  • If the z-score is negative and you are performing a lower-tailed test, use the table or software to find the area to the left of the z-score.
  • For a two-tailed test:
  • Find the area to the right of the z-score and double it if the z-score is positive.
  • Find the area to the left of the z-score and double it if the z-score is negative.
  • Subtract the area obtained (step 6 or step 7) from 1 to find the p-value.

    • So, to find the p-value from a z-score and significance level, you need to compare the z-score with the critical values and determine the area in the tail(s) depending on the type of test. Then, subtracting this area from 1 will give you the p-value.

    Frequently Asked Questions (FAQs):

    1. Can the p-value be greater than 1?

    No, the p-value cannot be greater than 1. It is a probability, and probabilities range from 0 to 1.

    2. What does a small p-value indicate?

    A small p-value (typically, less than the significance level) suggests strong evidence against the null hypothesis, indicating that the observed result is unlikely to have occurred by chance.

    3. What is the significance level?

    The significance level (alpha) is the predetermined threshold used to determine the statistical significance of a test. A common choice is 0.05, implying a 5% risk of rejecting the null hypothesis when it is true.

    4. How do I know which critical value to use?

    You can determine the critical value based on the desired significance level and the type of test (one-tailed or two-tailed). Either use a standard normal distribution table or statistical software to find the appropriate critical value.

    5. Is the p-value the same as the level of significance?

    No, the p-value and the level of significance are distinct. The p-value is the probability of obtaining a test statistic as extreme as the observed, assuming the null hypothesis is true. The level of significance is the threshold used to make a decision about the null hypothesis.

    6. How do I interpret the p-value?

    If the p-value is less than or equal to the significance level (alpha), you have sufficient evidence to reject the null hypothesis. If the p-value is greater than the significance level, you fail to reject the null hypothesis.

    7. What happens if the z-score is zero?

    If the z-score is zero, it means the observation or test statistic is exactly at the mean. The p-value will depend on the significance level and the type of test conducted.

    8. Can I find the p-value directly from a z-table?

    No, the z-table provides values corresponding to the cumulative probability from negative infinity up to a z-score. To find the p-value, you need to calculate the area in the tail(s) based on the type of test.

    9. Is the p-value always symmetric for a two-tailed test?

    Yes, for a two-tailed test, the p-value is always symmetric. To obtain the p-value, you calculate the area in both tails and sum them.

    10. How are the p-value and confidence level related?

    The p-value and confidence level are inversely related. If the p-value is smaller than the significance level, the result is statistically significant, corresponding to a higher confidence level.

    11. Can the p-value be negative?

    No, the p-value cannot be negative. It represents a probability, and probabilities are non-negative values.

    12. Can I determine statistical significance only based on the p-value?

    No, statistical significance should be determined based on the p-value in combination with the significance level. The p-value alone does not dictate statistical significance; it is the comparison with the chosen significance level that determines significance or non-significance.

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