Using P-values to make conclusions (article) | Khan Academy (2024)

Learn how to use a P-value and the significance level to make a conclusion in a significance test.

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  • Stan

    6 years agoPosted 6 years ago. Direct link to Stan's post “Could any one explain how...”

    Could any one explain how to get the p-value in the second example?

    (19 votes)

    • Saxon Knight

      5 years agoPosted 5 years ago. Direct link to Saxon Knight's post “Sure!The p-value is the...”

      Using P-values to make conclusions (article) | Khan Academy (4)

      Using P-values to make conclusions (article) | Khan Academy (5)

      Using P-values to make conclusions (article) | Khan Academy (6)

      Sure!

      The p-value is the probability of a statistic at least as deviant as ours occurring under the assumption that the null hypothesis is true.

      Under that assumption, and noting also that we are given that the population is normally distributed (or that we took a sample size of at least 30 [by the Central Limit Theorem]), we can treat the sampling distribution of the sample mean as a normal distribution.

      So now, we can use the normal cumulative density function or a z-table to find this probability. (We could also use a t-table, but it is allowable to just use a z table since our sample size is larger than 30)

      To use a z-table, we'll need to find the appropriate z-score first.

      Since the answer to what we are asking comes from the sampling distribution of the sample mean, we would find the appropriate standard deviation to use by dividing the population standard deviation by the square root of the sample size (since the variance of the sampling distribution is the population variance divided by the sample size, and the standard deviation is the square root of the variance).

      That would give us a standard deviation for the sampling distribution of the sample mean.

      I say would, because unfortunately, we don’t always know the population standard deviation, and so (as it seems they did here, despite knowing the population standard deviation), we are using the sample standard deviation in its place to find an estimate of the standard deviation for the sampling distribution of the sample mean, which is also known as the standard error of the mean.

      In our example, the standard error of the mean therefore has a value of 0.12 / 50^0.5, or approximately 0.01697.

      Taking the difference between our sample mean and the population mean and dividing it by the standard error gives us our z-score (number of standard errors our sample mean is away from the population mean), which is approximately (7.36 - 7.4) / 0.01697 or -2.36.

      Since the alternative hypothesis is not specific about the population mean being either greater than or less than the value in the null hypothesis, we have to consider both tails of the distribution, but by symmetry of the standard normal distribution, we can accomplish this by simply doubling the value we get from using our obtained z-score with a z-table.

      The value given by a z-table using a z-score of -2.36 is 0.0091, which, when doubled, is 0.0182 or approximately 0.02.

      This (or other videos before it in that section) might also help (it comes later in this unit): https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/tests-about-population-mean/v/calculating-p-value-from-t-statistic

      :)

      (57 votes)

  • G.Gulzt

    6 years agoPosted 6 years ago. Direct link to G.Gulzt's post “I don't understand the p-...”

    I don't understand the p-value in example 1

    Isn't the calculation: binomial(60,20) * 0.75^40 * 0.25^20 = 0.0383?
    The problem states it is "0.068". Is this p-value wrong or did I make a mistake in my calculation?

    (6 votes)

  • Nishay

    6 years agoPosted 6 years ago. Direct link to Nishay's post “How do you decide what Si...”

    How do you decide what Significance level you should set??

    (1 vote)

    • Ian Pulizzotto

      6 years agoPosted 6 years ago. Direct link to Ian Pulizzotto's post “A significance level of 0...”

      Using P-values to make conclusions (article) | Khan Academy (13)

      A significance level of 0.05 (i.e. 5%) is commonly used, but sometimes other significance levels are used.

      Note that the significance level is the probability of a Type 1 error (rejecting a true null hypothesis). Everything else being equal, decreasing the significance level (probability of a Type 1 error) increases the probability of a Type 2 error (failing to reject a false null hypothesis), and vice versa.

      So the statistician has to weigh the cost of a Type 1 error (rejecting a true null hypothesis) versus the cost of a Type 2 error (failing to reject a false null hypothesis) in the real-world situation. If the statistician is especially concerned about the cost of a Type 1 error, then he/she will use a significance level that is less than 0.05. However, if instead the statistician is especially concerned about the cost of a Type 2 error, then he/she will use a significance level that is greater than 0.05.

      (12 votes)

  • Mohammad Yasser

    5 years agoPosted 5 years ago. Direct link to Mohammad Yasser's post “As far as I understand, r...”

    As far as I understand, rejecting H0 doesn't mean accepting Ha in all cases. Rejecting H0 only implies accepting Ha iff both are complements to each other, i.e. exactly one of them must be true. E.g. if H0 says x = 5, and Ha says x > 5, then maybe both are wrong and the truth is x < 5. This will be so weird though because the truth is expected to be either H0 or Ha, but I think it's theoretically possible to happen.

    (6 votes)

    • Nick Barnes

      a year agoPosted a year ago. Direct link to Nick Barnes's post “You're confounding the tr...”

      You're confounding the truthfulness of H0 with the acceptability of Ha. In your example, not accepting Ha says we will not accept that x > 5, in other words x = 5 or x < 5. Not accepting Ha does not report on the truth that x < 5, it still allows the possibility that x = 5 - that is H0 is not rejected. It's very tempting to say H0 is "rejected" because x = 5 is a false statement. The key is to clarify what is meant by "reject". The statistics notion of reject is not based on whether the hypothesis is a true or false statement but on if it is rejected by the acceptability criteria of Ha.

      From that perspective verify these statements (the logic flows from one to the next): If you do not accept Ha, then you do not reject H0. The only way you can reject H0 is by accepting Ha. It doesn't make sense to both reject H0 and not accept Ha.

      (1 vote)

  • VVCephei

    6 years agoPosted 6 years ago. Direct link to VVCephei's post “In the first problem, is ...”

    In the first problem, is 0.068 the correct p-value? Assuming that the null hypothesis is true, and p = 0.25, the sampling distribution of sample proportion with n = 60 should be approximately normal, with a mean = p = 0.25 and standard deviation of √((p·(1-p))/n) ≈ 0.056. So a sample with p-hat = 0.3 should only have a z-score ≈ 0.89, and there should be ≈ 0.187 probability of getting a sample with p-hat ≥ 0.3. Or am i missing something?

    (2 votes)

    • Ian Pulizzotto

      6 years agoPosted 6 years ago. Direct link to Ian Pulizzotto's post “You generally had the rig...”

      You generally had the right idea for calculating the p-value. Note that the p-hat value is not 0.3, but rather 20/60 = 1/3 = 0.3333... (perhaps you did not consider the bar on top of the decimal digit 3). So the z-score is about 1.49 instead of 0.89. The probability of equaling or exceeding a z-score of 1.49 is about 0.068.

      Have a blessed, wonderful day!

      (8 votes)

  • JorgeMercedes

    6 years agoPosted 6 years ago. Direct link to JorgeMercedes's post “Please please please show...”

    Please please please show us how those P Values come about. We are very troubled.

    (2 votes)

    • mzg23patel

      6 years agoPosted 6 years ago. Direct link to mzg23patel's post “the p values are generall...”

      the p values are generally given whenever such problems are asked, i think calculating p values is a completely unrelated concept here so it is not taught

      (5 votes)

  • A_meginniss

    a year agoPosted a year ago. Direct link to A_meginniss's post “what is the equation to c...”

    what is the equation to calculate the p value

    (3 votes)

    • daniella

      3 months agoPosted 3 months ago. Direct link to daniella's post “The equation to calculate...”

      The equation to calculate the p-value depends on the specific hypothesis test being performed. For example:
      In a z-test for a population mean, the p-value can be calculated using the standard normal distribution tables or software functions.
      In a t-test for a population mean, the p-value is typically calculated using the t-distribution tables or software functions.
      In a chi-square test for independence, the p-value is calculated based on the chi-square distribution.
      Each test has its own formula for calculating the p-value based on the observed sample data and the assumptions of the test.

      (1 vote)

  • Junsang

    5 years agoPosted 5 years ago. Direct link to Junsang's post “ur... are we going to be ...”

    ur... are we going to be told how to calculate this P-value?

    I'm confused on what it actually is...

    (2 votes)

    • Jerry Nilsson

      5 years agoPosted 5 years ago. Direct link to Jerry Nilsson's post “Yes, there are lessons on...”

      Yes, there are lessons on how to calculate the p-value, which is the probability that the assumed population parameter is true, based on a sample statistic of that parameter.

      (2 votes)

  • ricardoadam_

    4 years agoPosted 4 years ago. Direct link to ricardoadam_'s post “First problem, question B...”

    First problem, question B, remark for answer C
    "There wasn't enough evidence to reject H0 at this significance level, but that doesn't mean we should accept H0. This experiment didn't attempt to collect evidence in support of H0."

    What would be like an experiment that would collect evidence in support of H0?

    (2 votes)

    • Bryan

      4 years agoPosted 4 years ago. Direct link to Bryan's post “This experiment just assu...”

      This experiment just assumed Ho was true; if p-value was below our sig level, then our assumption of Ho could be rejected, since it's unlikely we'd get such a deviant (or more deviant) sample proportion if Ho was true.
      If p-value was above our sig level, it tells us that Ha can be rejected, since it's likely enough to get a sample proportion of 0.333333333etc or more assuming Ho; there is no need for Ha to be true (no need for pop proportion to be higher).

      But Ha being rejected doesn't prove Ho (pop proportion = 0.25).

      For example, our hypothesis could be
      Ho: p = 0.245
      Ha: p > 0.245

      And then with a p^ of 0.33333etc, we would have a p-value of around 0.056, which still above our sig level, meaning that we reject our Ha, p > 0.245.
      This would be a contradiction if our first Ho was proven, but it wasn't, so it's not a contradiction.
      Notice how rejecting p > 0.245 doesn't conflict with rejecting p > 0.25, since we never said p had to be in between 0.245 and 0.25.

      You could maybe use the law of large numbers and coerce millions of people into guessing the water in your cups, and see if that proportion is really close to 0.25 to possibly prove that p = 0.25. There's probably a better experiment, but I'm not too experienced in thinking of them :P

      (1 vote)

  • brittshi000

    6 months agoPosted 6 months ago. Direct link to brittshi000's post “Thank you for the great q...”

    Thank you for the great questions. They helped me so much to prepare for my test.

    (2 votes)

Using P-values to make conclusions (article) | Khan Academy (2024)

FAQs

How do we use p values to make conclusions? ›

A p-value less than 0.05 is typically considered to be statistically significant, in which case the null hypothesis should be rejected. A p-value greater than 0.05 means that deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected.

What do you compare the p-value to? ›

We compare a P-value to a significance level to make a conclusion in a significance test. Given the null hypothesis is true, a p-value is the probability of getting a result as or more extreme than the sample result by random chance alone.

What if p-value is equal to significance level? ›

A p-value less than or equal to your significance level (typically ≤ 0.05) is statistically significant. A p-value less than or equal to a predetermined significance level (often 0.05 or 0.01) indicates a statistically significant result, meaning the observed data provide strong evidence against the null hypothesis.

What is the test of statistical significance? ›

Tests for statistical significance are used to estimate the probability that a relationship observed in the data occurred only by chance; the probability that the variables are really unrelated in the population. They can be used to filter out unpromising hypotheses.

How do you make a decision based on p-value? ›

Decision making with p-value

We compare p-value to significance level(α ) for taking a decision on Null Hypothesis. If p-value is greater than alpha, we do not reject the null hypothesis. If p-value is smaller than alpha, we reject the null hypothesis.

What is the p-value at a 0.05 What is your conclusion? ›

Question: With α = 0.05, what is your hypothesis testing conclusion? The conclusion is made by comparing α and the found p-value. If the p-value is less than or equal to α, the null hypothesis is rejected in favor of the alternative. If the p-value is greater than α, we fail to reject the null hypothesis.

What does p-value tell you? ›

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.

What conclusion should be made at the 0.05 level? ›

For example, when performing a statistical hypothesis test, if the significance level is set to 0.05 and the calculated significance probability is 0.002, the set null hypothesis is rejected and the conclusion is made with the content of the alternative hypothesis.

What is the biggest factor in determining your conclusion? ›

Among the given factors it is p value that is major in determination of the conclusion of the experiment. p value gives an about whether we can accept or reject a null hypothesis. Hence it works as an evidence against null hypothesis.

How do you explain p-value to non-technicians? ›

Academically, the P-value is the probability of obtaining results as extreme as the observed data, assuming that the null hypothesis is correct1.

What is the conclusion if p-value is less than significance level? ›

If your P value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample gives reasonable evidence to support the alternative hypothesis.

What if p-value is greater than 0.05 in regression? ›

A high P-value (> 0.05) means that we cannot conclude that the explanatory variable affects the dependent variable (here: if Average_Pulse affects Calorie_Burnage). A high P-value is also called an insignificant P-value.

What does it mean if something is not statistically significant? ›

This means that the results are considered to be „statistically non-significant‟ if the analysis shows that differences as large as (or larger than) the observed difference would be expected to occur by chance more than one out of twenty times (p > 0.05).

How big of a sample size do I need to be statistically significant? ›

Most statisticians agree that the minimum sample size to get any kind of meaningful result is 100. If your population is less than 100 then you really need to survey all of them.

What is a reasonable value for level of significance? ›

Many current research articles specify an alpha of 0.05 for their significance level. It cannot be stated strongly enough that there is nothing special, mathematical, or certain about picking an alpha of 0.05.

How do P values help us have confidence that the study results are? ›

The p-value is the probability that the observed effect within the study would have occurred by chance if, in reality, there was no true effect. Conventionally, data yielding a p<0.05 or p<0.01 is considered statistically significant.

What does your p-value make inferences about? ›

The purpose is to make inferences about population parameter by analyzing differences between observed sample statistic and the results one expects to obtain if some underlying assumption is true.

What is the purpose of p-value in research? ›

The p value is a number, calculated from a statistical test, that describes how likely you are to have found a particular set of observations if the null hypothesis were true. P values are used in hypothesis testing to help decide whether to reject the null hypothesis.

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