## Explain the p-value by explaining the statistical terms and experimenting with a simple fact, in which case 75% accuracy is statistically insignificant

norteNumerous experiments have been carried out in the cumulative advancement of current science, and articles have been published. While some of these experiments contributed to our success, some of them failed in practice and could not contribute to development, although they had successful results experimentally. So how do we decide how significant the findings of an experiment are? What should the findings be compared to? This article involves statistical terms such as p-value, null hypothesis, statistical significance case, and explains the Lady Tasting Tea experiment, as well as testing it with the p-value, including results and solutions.

It is a concept that should be known by anyone who follows scientific articles in areas such as biology, psychology, sociology, economics, criminology and wants what they read to predominate. Expressions such as p > 0.05, p < 0.05 are often found in scientific articles. One must first understand hypothesis testing and the potential erroneous results that can be drawn from these tests to understand the basis for these claims.

null hypothesis:It is a hypothesis that indicates the opposite of the result expected by the researcher in the investigation, that is, the opposite of the alternative hypothesis. That is, contrary to what the theory says, it assumes the value of H0 as the null hypothesis.

**Why does the idea contrary to the sustained hypothesis arise?**

In the philosophy of logic there is a technique called`reductio ad absurdum`

. This method is as old as*Aristotle's Prior Analytic*. It is to prove the falsity of a judgment that we want to prove it by presenting the contrary.

reductio ad absurdum: Instead of proving the opposite wrong to show that an opinion is true; It may be more accurate to refute this contrary opinion by making it seem absurd with absurdly extreme examples rather than using logical arguments.

It was also accepted in the last century that it is more reasonable to proceed on the principle of falsification in the philosophy of science. If a statistically significant relationship between two variables is sought, it is easier to argue that there is no such relationship and falsify it. EITHER*null hypothesis*it is presented to be forged, but whether its forgery succeeds or fails, there is no complete proof. EITHER*null hypothesis*may or may not be rejected. The hypothesis to be tested is`alternative hypothesis`

, abbreviated as “H1 o Ha”.

The value we call`p value`

; In its simplest definition, the null hypothesis is a measure of how mathematically possible the result we obtain is. The lower our result, the stronger the evidence against the null hypothesis.

**In summary, when you see the expression p < 0.05 in the articles you read, you can understand that there is a relationship that is considered statistically significant.**

Statistically significant: as its name indicates, it means that the result obtained is statistically significant and acceptable. To illustrate with an example, let's say a survey asks people if they like pizza. The pizza lover rate was 51% and the pizza aversion rate was 49%. Based on these results (51>49), it is not statistically correct to say that people like pizza. Due to the confidence interval used and possibly the sample size, it is understood that 51% is not large enough for this analysis like 49%, so the difference is not significant enough.

## Why the p-value = 0.05?

Arbitrarily. He was chosen arbitrarily by Sir Ronald Fisher, considered the father of modern statistics. He gave a class and entered a value of 5% as a dividing line to define it. An urban legend told to support this expression is the following:

if i toss a coin**once**and it comes up heads, do you think both sides of this coin are heads?**(1/2 = 0,5)**

And if I throw the coin**twice**and it comes out both times?**(1/4 = 0,25)**

And if**three times**?**(1/8 = 0,125)**

And if**quadruple**?**(1/16 = 0,0625)**

And if**five times**?**(1/32 = 0,03125)**

When a group of people were asked these questions, hardly anyone was suspicious the first 3 times, a group of people were suspicious the fourth time, and the vast majority thought the coin was fraudulent the fifth time. Therefore, 0.05 was chosen as the cut-off value. So is there a statistically significant difference between 0.0500001 and 0.4999999? Of course not, and the gray tones of life appear here too.

Take the experiment where 75% accuracy is statistically insignificant in the first part of Ronald Fisher's The Design of Experiment.

In the experiment, a woman claims that by tasting a cup of milk tea she can tell whether milk or tea was put into the cup first. The experimental setup is as follows: milk tea is poured into 8 glasses, milk is poured into 4 of them first, and tea is poured into the remaining 4 glasses first. The goal is to calculate the number of cups that the woman can guess correctly by chance alone, using the cup into which 4 milks and 4 teas are first poured, and make an inference about the accuracy of the statement. The woman's task is to divide the cups into two groups according to the order in which the tea and milk are served. To do this, she must correctly classify and select 4 cups from the same group.

Here, the null hypothesis is that the woman does not have that talent, and an inference can be made by reasoning about the p-value in the experiment statistics. Therefore, it is necessary to assume that the woman does not have such a talent, and calculate the ratio of possible hits for all probabilities, which can occur completely randomly.

There are 8 glasses in total and 4 of them will be selected because there are 2 labels and when 4 of them are placed in the correct place, the remaining 4 will automatically be in the correct place:

- For the first option, there are 8 possibilities.
- For the 2nd choice, 1 of them selected, there are 7 possibilities.
- For the 3rd option, 2 of them selected, there are 6 possibilities.
- For the 4th option, 3 of them selected, there are 5 possibilities.

Total number of possibilities 8 x 7 x 6 x 5 = 1680

The order of the cups selected from each other is as follows:

- One of the 4 glasses can be placed in the 1st row.
- One of the 3 cups can be placed in the second row.
- One of the 2 cups can be placed in the 3rd row.
- One of the 1 glass can be placed in the 4th row.

The sum of their displacements: 4 x 3 x 2 x 1 = 24

**The total selection number is 1680/24 = 70.**

Of course, we could do this with the simple combination operation in mathematics. Combination (8,4) = 8! / (4! x 4!) = 70.

Mathematically,

- The probability that the woman places the 4 glasses in the wrong group is 1/70 = 0.014 or
**1,4%** - The probability of putting the 3 glasses in the wrong group is 16/70 = 0.229 or
**22,9%** - The probability of putting half of them in the wrong group is 36/70 = 0.514 or
**51,4%** - The probability of making only 1 error is 16/70 = 0.229, or
**22,9%** - The probability of ordering them all correctly is 1/70 = 0.014 or
**1,4%** - The probability of at least 3 out of 4 successes (1+16)/70 = 0.243 or
**24,3%**

It can be said that the p value determines whether the result is statistically significant. If the result obtained is less than 0.05 (5%), the null hypothesis is rejected, that is, the result found is interpreted as statistically significant.

The case that all vessels are correctly positioned, ie 0.014, is statistically significant (because 0.014 < 0.05). On the other hand,**the case that at least 3 out of 4 glasses are placed correctly, that is, 0.243, is not statistically significant**based on the p-value (due to 0.243>0.05), it is considered statistically insignificant if the woman predicts 3 out of 4 cups. This means that a single mistake made by the woman will reduce her performance below the significant level. In this case, the experiment is repeated or the elements are expanded.

How many of us can predict 3 out of 4 correctly?Here is the linkfor an article in which scientists oppose statistical significance

## Resources

- R.A.Fisher Design of Experiments (1935): the principles of experimentation, illustrated by a psychophysical experiment

## Other reading

What is the meaning of e?

## FAQs

### What does p-value of .05 mean? ›

"A P value of 0.05 does not mean that there is a 95% chance that a given hypothesis is correct. Instead, it signifies that **if the null hypothesis is true, and all other assumptions made are valid, there is a 5% chance of obtaining a result at least as extreme as the one observed**.

**What does p-value of 0.05 mean quizlet? ›**

P Value. **the probability that observed differences could be due to chance**. if p value is less than 0.05. we can reject the null hypothesis when this is true, the result is "statistically significant" and therefore is unlikely to be due to chance. if p value is greater than 0.05.

**What is the meaning of 0.05 level of significance? ›**

The significance level is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates **a 5% risk of concluding that a difference exists when there is no actual difference**.

**Why p-value is not enough? ›**

The p value has been increasingly criticized when used alone in reporting results, particularly in medical research. One of its major limitations is that **it only indicates whether or not the null hypothesis is true, but does not provide information about the magnitude of the effect or the extent of change**.

**What does p 0.05 mean in t test? ›**

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.

**What does p-value tell you? ›**

The p-value is **the probability that the null hypothesis is true**. (1 – the p-value) is the probability that the alternative hypothesis is true. A low p-value shows that the results are replicable. A low p-value shows that the effect is large or that the result is of major theoretical, clinical or practical importance.

**What does p .05 or α .05 actually mean? ›**

A common rule is that when the probability is less than 5% (i.e.,p < . 05) that a sample mean drawn from the null population would be as large as the obtained sample mean, we conclude that the sample did not come from the null population. This probability criterion (e.g., . 05) is called alpha (α).

**What does the significance at the 0.05 level mean quizlet? ›**

Remember that, typically, the alpha is 0.05, which means that **if you find a difference, you are 95% sure it is truly there, not just a chance occurrence**. Null hypothesis. No difference or association between variables that is any greater or less than would be expected by chance. - represented as H0.

**What does a .05 level of significance mean quizlet? ›**

a .05 level of significance means that: **there is only a 5 percent chance that a statistic's value could be obtained as a result of random error**.

**What does a 0.05 significance level correspond with in confidence 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.

### What does it mean when you use a 0.05 level of significance to evaluate statistical results quizlet? ›

What does a ". 05 level of significance" mean? **There is a less than 5% chance that the result would occur when the null hypothesis is true**.

**Is p-value less than 0.05 is good? ›**

A p-value less than 0.05 (typically ≤ 0.05) is **statistically significant**. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random).

**What is the best way to describe p-value? ›**

What exactly is a p value? 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.

**How much does the p-value have to be to be significant? ›**

If the p-value is **under .** **01**, results are considered statistically significant and if it's below . 005 they are considered highly statistically significant.

**Do you reject the null hypothesis at the 0.05 significance level? ›**

In the majority of analyses, an alpha of 0.05 is used as the cutoff for significance. **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.**

**What does p-value mean in simple terms? ›**

A p-value is a statistical measurement used to validate a hypothesis against observed data. A p-value measures the probability of obtaining the observed results, assuming that the null hypothesis is true. The lower the p-value, the greater the statistical significance of the observed difference.

**What is p-value and why is it important? ›**

The P value means **the probability, for a given statistical model that, when the null hypothesis is true, the statistical summary would be equal to or more extreme than the actual observed results** [2].

**What does p-value less than 0.05 mean? ›**

A p-value of 0.05 or less means that, if the null hypothesis were true, the probability of seeing the observed differences, or more extreme differences, is 5% or less, assuming that the results are not distorted by bias or confounding.

**What does p 0.055 mean? ›**

Usually statistical significance in this context is defined as a pre-set P-value <0.05. A p-value of 0.055 is considered **not statistically significant**.

**Why is an alpha level of .05 commonly used? ›**

In most cases, researchers use an alpha of 0.05, which means that **there is a less than 5% chance that the data being tested could have occurred under the null hypothesis**.

### How do you reject null hypothesis? ›

Rejecting the Null Hypothesis

Reject the null hypothesis **when the p-value is less than or equal to your significance level**. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go!

**What is the critical value of the 0.05 level of significance in two tailed test? ›**

The most commonly used significance level is α = 0.05. For a two-sided test, we compute 1 - α/2, or 1 - 0.05/2 = **0.975** when α = 0.05. If the absolute value of the test statistic is greater than the critical value (0.975), then we reject the null hypothesis.

**When using a significance level of 0.05 How often will you reject hypotheses that are actually correct? ›**

6.3 - Issues with Multiple Testing

If we are conducting a hypothesis test with an level of 0.05, then we are accepting a **5%** chance of making a Type I error (i.e., rejecting the null hypothesis when the null hypothesis is really true).

**What is the critical value of the 0.05 level of significance in left tailed test? ›**

For a left-tail test at the 0.05 level of significance, the critical value is **z _{α} = − 2.33**.

**What does it mean if results are statistically significant? ›**

“Statistical significance helps quantify whether a result is likely due to chance or to some factor of interest,” says Redman. When a finding is significant, it simply means **you can feel confident that's it real, not that you just got lucky (or unlucky) in choosing the sample**.

**What does it mean to reject the null hypothesis at the 0.05 level quizlet? ›**

Level of 0.05. This means that **if the P value is less than 0.05**, you reject the null hypothesis; if P is greater than or equal to 0.05, you don't reject the null hypothesis. Increase your chance of a false positive but decrease chance of false negative.

**What is the critical value at the 0.05 level of significance for a goodness? ›**

Assuming the chi-square test is applied as goodness of fit test. At the degree of freedom and level of significance 0.05, the critical value say (χ2crit) ( χ 2 c r i t ) is obtained using chi-square table. Hence, the critical value is **11.070**.

**Is p-value 0.05 Enough A study on the statistical evaluation of classifiers? ›**

This section shows, using real-world case studies, that just checking the condition **p-value < 0.05 is not enough for a sound statistical analysis** and can mislead researchers to ignore relevant results or to value a non-relevant result.

**Why is a statistical significance or probability of .05 most often used in research studies? ›**

Within the social sciences, researchers often adopt a significance level of 5%. This means researchers are only willing to conclude that the results of their study are statistically significant if the probability of obtaining those results if the null hypothesis were true—known as the p value—is less than 5%.

**When to use the 0.01 and the 0.05 level of significance? ›**

The degree of statistical significance generally varies depending on the level of significance. 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**.

### How do you explain the p-value example? ›

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.

**How do you interpret the p-value for dummies? ›**

A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

**How do you use p-value in hypothesis testing? ›**

Set the significance level, , the probability of making a Type I error to be small — 0.01, 0.05, or 0.10. Compare the P-value to . If the P-value is less than (or equal to) , reject the null hypothesis in favor of the alternative hypothesis. If the P-value is greater than , do not reject the null hypothesis.

**What does p-value of 0.05 mean 95 %? ›**

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**.

**What does p-value of .04 mean? ›**

In this context, what P = 0.04 (i.e., 4%) means is that if the null hypothesis is true and if you perform the study a large number of times and in exactly the same manner, drawing random samples from the population on each occasion, then, on 4% of occasions, you would get the same or greater difference between groups ...

**What does p-value of .06 mean? ›**

A p value of 0.06 means that **there is a probability of 6% of obtaining that result by chance when the treatment has no real effect**. Because we set the significance level at 5%, the null hypothesis should not be rejected.

**What does p-value tell you that confidence interval does not? ›**

P-values are clearer than confidence intervals. It can be judged **whether a value is greater or less than a previously specified limit**. This allows a rapid decision as to whether a value is statistically significant or not.

**What is p-value in simple words? ›**

A p-value is **a statistical measurement used to validate a hypothesis against observed data**. A p-value measures the probability of obtaining the observed results, assuming that the null hypothesis is true. The lower the p-value, the greater the statistical significance of the observed difference.

**What does p-value of less than 0.05 mean? ›**

A p-value of 0.05 or less means that, if the null hypothesis were true, the probability of seeing the observed differences, or more extreme differences, is 5% or less, assuming that the results are not distorted by bias or confounding.

**How do you reject a null hypothesis? ›**

Rejecting the Null Hypothesis

Reject the null hypothesis **when the p-value is less than or equal to your significance level**. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go!