p-value - easily explained with an example

DATAtab
29 Nov 202208:10
EducationalLearning
32 Likes 10 Comments

TLDRThis video script delves into the concept of the p-value in statistical analysis. It begins with an example comparing the height of the average American man to that of an American basketball player, using a null hypothesis that assumes an average height of 1.77 meters. The script explains that a sample will likely differ from this average by some margin, and the p-value quantifies the probability of observing such a deviation by chance if the null hypothesis were true. A low p-value suggests strong evidence against the null hypothesis, prompting its rejection in favor of the alternative hypothesis that there is a difference. The significance level, or alpha level, is set before the study to determine when the p-value is low enough to reject the null hypothesis. Commonly set at 0.05 or 0.01, it helps maintain comparability across studies. The script also touches on the risks of type 1 and type 2 errors and concludes with a demonstration of how to calculate p-values for various hypothesis tests using an online tool called Data Tab.

Takeaways
  • 🏀 **Null Hypothesis**: The average height of an American basketball player is assumed to be 1.77 meters, which is the same as the average American man.
  • 📐 **Sample Deviation**: A sample of basketball players will likely not have an exact mean height of 1.77 meters due to random variation.
  • 🎯 **Undirected Hypothesis**: The test is undirected, meaning it is only concerned with whether there is a difference in height, not the direction of that difference.
  • 🔍 **P-Value Definition**: The p-value indicates the likelihood of drawing a sample that deviates from the population mean by an equal or greater amount than the observed sample mean.
  • 📊 **Significance Level (Alpha)**: This is the threshold for determining whether the null hypothesis is rejected. It is set before the study and is typically at 5% or 1%.
  • ⚖️ **Hypothesis Rejection**: A small p-value (typically less than 0.05) provides evidence to reject the null hypothesis in favor of the alternative hypothesis, which assumes a difference.
  • 🚫 **Type 1 Error**: The risk of wrongly rejecting the null hypothesis when it is actually true, which occurs if the p-value is smaller than the significance level by chance.
  • 🔁 **Type 2 Error**: The risk of not rejecting the null hypothesis when it is false, which can happen if the p-value is larger than the significance level despite a real difference.
  • 🌐 **Online Tools**: Data tab is an online tool that can calculate p-values for various hypothesis tests, such as t-tests, chi-square tests, ANOVA, and non-parametric tests.
  • 📋 **Data Input**: Users can input their data into Data tab for automated suggestions and calculations of appropriate hypothesis tests.
  • 📝 **Interpretation**: Data tab provides interpretation in words for the results of hypothesis tests, aiding in understanding whether to reject the null hypothesis based on the data.
Q & A

  • What is the main topic of the video?

    -The main topic of the video is to explain the concept of the p-value and how it is interpreted in statistical hypothesis testing.

  • What is the example used in the video to illustrate the concept of p-value?

    -The example used is to investigate whether there is a difference in height between the average American man and the average American basketball player.

  • What is the null hypothesis in the given example?

    -The null hypothesis is that the average height of an American basketball player is 1.77 meters, assuming no difference in height compared to the average American man.

  • Why is it unlikely to get an exact mean from the sample?

    -It is unlikely because samples are drawn from the population and due to random variation, they may deviate from the actual population mean by some amount.

  • What does the p-value represent in the context of hypothesis testing?

    -The p-value represents the probability of obtaining a sample that deviates from the population mean by an equal or greater amount than the observed value, assuming the null hypothesis is true.

  • What does a low p-value suggest about the null hypothesis?

    -A low p-value suggests that the observed sample deviation from the population mean is unlikely to have occurred by chance alone, providing evidence against the null hypothesis.

  • What is the significance level, also known as the alpha level?

    -The significance level, or alpha level, is the threshold for the p-value that determines whether the null hypothesis is rejected. It is set before conducting the study and is commonly at 5% or 1%.

  • What is considered a significant result in terms of p-value?

    -A p-value of less than 5% is considered significant, and a p-value of less than 1% is considered highly significant.

  • What are the types of errors associated with hypothesis testing?

    -Type 1 error is rejecting the null hypothesis when it is actually true. Type 2 error is not rejecting the null hypothesis when it is actually false.

  • How can one calculate the p-value for various hypothesis tests online?

    -One can use online tools like Data Tab by visiting data.net, entering their data, and selecting the appropriate hypothesis test for their variables.

  • What does it mean if the p-value is larger than the significance level?

    -If the p-value is larger than the significance level, it means that there is not enough evidence to reject the null hypothesis, and the observed difference could be due to chance.

  • How can the interpretation of the p-value be aided online?

    -Online tools like Data Tab provide an 'interpretation in words' feature that offers a clear explanation of the results of a hypothesis test, aiding in the understanding of the p-value.

Outlines
00:00
🏀 Understanding the P-value and Hypothesis Testing

This paragraph introduces the concept of the p-value and its role in hypothesis testing. It uses the example of comparing the average height of American men to basketball players. The null hypothesis is set, assuming the average height of basketball players is 1.77 meters. The paragraph explains that a sample will likely not yield an exact mean due to random variation. The p-value is then defined as the probability of drawing a sample that deviates from the population mean by an equal or greater amount than the observed sample mean. The significance of a low p-value in rejecting the null hypothesis is discussed, along with the concept of a significance level (alpha level), which is predetermined before the study. The paragraph concludes by emphasizing that a small p-value provides evidence against the null hypothesis, but it is always a probability and not a certainty.

05:04
📊 Significance Levels and Errors in Hypothesis Testing

The second paragraph delves into the significance level, which is set at a conventional 5% or 1%. It explains that a p-value less than 1% is considered highly significant, while a p-value less than 5% is termed significant. If the p-value exceeds 5%, the result is deemed not significant. The paragraph also discusses the implications of rejecting or failing to reject the null hypothesis based on the p-value, and the potential for type 1 and type 2 errors. These errors occur when the null hypothesis is wrongly rejected (type 1) or not rejected when it is actually false (type 2). The paragraph concludes with a demonstration of how to calculate the p-value for various hypothesis tests online using a tool like Data Tab, which can suggest appropriate tests based on the variables selected and provide interpretations of the results.

Mindmap
Keywords
💡p-value
The p-value is a statistical measure that indicates the probability of obtaining results as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. In the video, it is used to determine the likelihood of drawing a sample that deviates from the population mean by an equal or greater amount than the observed sample mean. For instance, if the p-value is 0.03, it implies there is a 3% chance of observing a sample mean that deviates by 9 centimeters or more from the hypothesized population mean of 1.77 meters.
💡null hypothesis
The null hypothesis is a statement that there is no significant difference between groups or variables in a study. It serves as a baseline assumption that researchers test against. In the context of the video, the null hypothesis is that the average height of an American basketball player is 1.77 meters, which is the same as the average height of an American man. The video discusses how the p-value helps in deciding whether to reject or accept this null hypothesis.
💡alternative hypothesis
The alternative hypothesis is a statement that proposes a different outcome from the null hypothesis. It is what researchers accept if the null hypothesis is rejected based on statistical evidence. The video contrasts the null hypothesis with the alternative hypothesis, which assumes that there is a difference in height between the average American man and the average American basketball player.
💡significance level
The significance level, also known as alpha level, is a threshold probability used to decide whether to reject the null hypothesis. It is determined before conducting a study and is typically set at 5% or 1%. If the p-value is less than the significance level, the null hypothesis is rejected. The video explains that a significance level of less than 1% is considered highly significant, while less than 5% is simply significant.
💡sample
A sample is a subset of a population that is used for statistical analysis. In the video, the concept of a sample is central to understanding how researchers use it to make inferences about a larger population. The video discusses how a sample of American basketball players is taken to investigate if their average height differs from that of the average American man.
💡type 1 error
A type 1 error occurs when the null hypothesis is incorrectly rejected even though it is actually true. In the video, this is illustrated by the scenario where the mean height of basketball players is indeed 1.77 meters, but a sample happens to be far enough away to result in a p-value smaller than the significance level, leading to a false rejection of the null hypothesis.
💡type 2 error
A type 2 error happens when the null hypothesis is not rejected even though it is false. The video explains this by saying that if the mean height of basketball players is not 1.77 meters, but a sample by chance is very close to that value, the p-value might be larger than the significance level, leading to a failure to reject the null hypothesis when it should be.
💡sample deviation
Sample deviation refers to how much a sample's mean differs from the population mean. The video uses this concept to discuss how the p-value quantifies the likelihood of observing a sample mean that deviates from the hypothesized population mean by an equal or greater amount than the observed sample.
💡statistical hypothesis test
A statistical hypothesis test is a method used to make decisions about population parameters based on sample data. The video focuses on how the p-value is calculated within the context of a hypothesis test to determine whether there is a significant difference in height between two groups, in this case, American men and American basketball players.
💡normally distributed data
Normally distributed data refers to a data set where values are symmetrically distributed around a mean, following a Gaussian or normal distribution. The video mentions this in the context of interpreting the p-value, noting that for normally distributed data, the probability that the mean lies in a certain range is split equally in both directions from the mean.
💡data tab
Data tab is a hypothetical statistical software mentioned in the video that calculates the p-value for various hypothesis tests. The video script provides an example of how to use this software to conduct a t-test for independent samples or an analysis of variance (ANOVA), depending on the variables selected, and to interpret the resulting p-value.
Highlights

The video discusses the concept and interpretation of the p-value in statistical hypothesis testing.

An example is used to illustrate the difference in height between the average American man and basketball player.

The average height of an American man is stated as 1.77 meters for the purpose of the null hypothesis.

The null hypothesis assumes that the average height of American basketball players is also 1.77 meters.

A sample is drawn from the population of American basketball players to test the null hypothesis.

The p-value measures the likelihood of drawing a sample that deviates from the population mean by an equal or greater amount than observed.

The significance of the p-value is that it indicates the strength of evidence against the null hypothesis.

A p-value of 0.03 suggests that there is a 3% chance of observing a sample mean that deviates by 9 centimeters or more from the population mean.

The significance level, or alpha level, determines when the p-value is small enough to reject the null hypothesis.

The significance level is set before the study and is typically at 5% or 1% for comparability.

A p-value less than 1% is considered highly significant, less than 5% is significant, and greater than 5% is not significant.

The null hypothesis is rejected if the p-value is smaller than 0.05, assuming the significance level is set at 5%.

There is a possibility of type 1 error, which is rejecting the null hypothesis when it is actually true.

Type 2 error occurs when the null hypothesis is not rejected despite it being false.

Data tab is introduced as a tool for calculating p-values for various hypothesis tests online.

Data tab suggests appropriate hypothesis tests based on the variables selected by the user.

The p-value can be found after conducting a hypothesis test on Data tab, and interpretation can be provided in words.

An example of using Data tab for a t-test for independent samples and an analysis of variance is provided.

Non-parametric counterparts can also be calculated if the data is not normally distributed.

The video concludes with a summary of the p-value's role in hypothesis testing and the importance of the significance level.

Transcripts

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P-valueHypothesis TestingStatistical SignificanceNull HypothesisType 1 ErrorType 2 ErrorData AnalysisSample DeviationSignificance LevelBasketball PlayersAmerican MenHeight Comparison