What is the relationship between confidence intervals and p values 2024?
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Lily Adams
Works at EcoVenture Consulting, Lives in Sydney, Australia.
As a statistical expert with a strong background in statistical analysis and data interpretation, I often come across the concepts of confidence intervals and p-values. These two statistical tools are commonly used in hypothesis testing to make inferences about a population from sample data. Understanding their relationship is crucial for anyone working with statistical data.
Confidence intervals provide a range of values that are likely to contain an unknown population parameter. It's a way to express the uncertainty of an estimate. For instance, if we're estimating the mean height of a population, a 95% confidence interval would mean that we are 95% confident that the true mean falls within that range. The width of the confidence interval is influenced by the level of confidence, the variability in the data, and the sample size. A wider interval indicates more uncertainty, while a narrower interval indicates more precision.
On the other hand, p-values relate to the strength of the evidence against the null hypothesis. The null hypothesis is a statement of no effect or no difference, and it's what we test against when we're trying to find evidence of an effect or a relationship. A p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from my sample data, assuming that the null hypothesis is true. A common threshold for significance is a p-value of 0.05, which means that there is a 5% chance that the observed results occurred by random chance if the null hypothesis were true.
Now, let's delve into the relationship between the two. While confidence intervals provide a range of plausible values for an estimate, p-values provide a measure of the strength of evidence against the null hypothesis. They are related in the sense that they both depend on the same underlying test statistic and the same assumptions. However, they serve different purposes and are interpreted differently.
A narrow confidence interval might suggest a precise estimate, but it doesn't necessarily mean that the evidence against the null hypothesis is strong. Similarly, a low p-value indicates strong evidence against the null hypothesis, but it doesn't tell us about the magnitude of the effect or the range of plausible values for the parameter.
The statement that "the wider the confidence interval on a parameter estimate is, the closer one of its extreme points will be to zero, and a p-value of 0.05 means that the 95% confidence interval just touches zero" is a bit misleading. It's true that a wider confidence interval might include zero, which could correspond to a p-value that is not significantly different from zero. However, the width of the confidence interval is not solely determined by the p-value. It's also influenced by the sample size and the variability in the data. Moreover, a p-value of 0.05 does not imply that the 95% confidence interval is at zero; rather, it suggests that there is a 5% probability that the true effect is zero, given the data and the assumptions made.
In conclusion, while confidence intervals and p-values are related and are both used in the context of hypothesis testing, they are not directly interchangeable. Each provides different information about the data and the strength of the evidence. It's important to consider both when making statistical inferences to get a more complete picture of the results.
Confidence intervals provide a range of values that are likely to contain an unknown population parameter. It's a way to express the uncertainty of an estimate. For instance, if we're estimating the mean height of a population, a 95% confidence interval would mean that we are 95% confident that the true mean falls within that range. The width of the confidence interval is influenced by the level of confidence, the variability in the data, and the sample size. A wider interval indicates more uncertainty, while a narrower interval indicates more precision.
On the other hand, p-values relate to the strength of the evidence against the null hypothesis. The null hypothesis is a statement of no effect or no difference, and it's what we test against when we're trying to find evidence of an effect or a relationship. A p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from my sample data, assuming that the null hypothesis is true. A common threshold for significance is a p-value of 0.05, which means that there is a 5% chance that the observed results occurred by random chance if the null hypothesis were true.
Now, let's delve into the relationship between the two. While confidence intervals provide a range of plausible values for an estimate, p-values provide a measure of the strength of evidence against the null hypothesis. They are related in the sense that they both depend on the same underlying test statistic and the same assumptions. However, they serve different purposes and are interpreted differently.
A narrow confidence interval might suggest a precise estimate, but it doesn't necessarily mean that the evidence against the null hypothesis is strong. Similarly, a low p-value indicates strong evidence against the null hypothesis, but it doesn't tell us about the magnitude of the effect or the range of plausible values for the parameter.
The statement that "the wider the confidence interval on a parameter estimate is, the closer one of its extreme points will be to zero, and a p-value of 0.05 means that the 95% confidence interval just touches zero" is a bit misleading. It's true that a wider confidence interval might include zero, which could correspond to a p-value that is not significantly different from zero. However, the width of the confidence interval is not solely determined by the p-value. It's also influenced by the sample size and the variability in the data. Moreover, a p-value of 0.05 does not imply that the 95% confidence interval is at zero; rather, it suggests that there is a 5% probability that the true effect is zero, given the data and the assumptions made.
In conclusion, while confidence intervals and p-values are related and are both used in the context of hypothesis testing, they are not directly interchangeable. Each provides different information about the data and the strength of the evidence. It's important to consider both when making statistical inferences to get a more complete picture of the results.
2024-06-16 15:56:55
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Works at the International Development Association, Lives in Washington, D.C., USA.
The p-value relates to a test against the null hypothesis, usually that the parameter value is zero (no relationship). The wider the confidence interval on a parameter estimate is, the closer one of its extreme points will be to zero, and a p-value of 0.05 means that the 95% confidence interval just touches zero.Oct 4, 2011
2023-06-18 04:17:48
Charlotte Robinson
QuesHub.com delivers expert answers and knowledge to you.
The p-value relates to a test against the null hypothesis, usually that the parameter value is zero (no relationship). The wider the confidence interval on a parameter estimate is, the closer one of its extreme points will be to zero, and a p-value of 0.05 means that the 95% confidence interval just touches zero.Oct 4, 2011
