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Statistics Calculators ▶ P Value from T Score Calculator

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**Table of Content**

An online p value calculator from t score helps you to calculate the p value of a sample accurately. Before we start using this calculator, let us have a proper guide to t score in the content of statistics.

**A t score refers to the deviation in data from the mean position.**

**For example:**

Let us discuss a real-life example of t score:

Suppose you are asked for **BMD** which is a test done to measure the bone density of an adult. After the test is performed, the score that you get is actually the deviation from the mean position.

When you have a very small sample **(<30)**, then you need to use t score formula given below:

**T = (X – μ) / [ σ/√(n) ]**

where;

**x** = sample mean

**μ**= population mean

**s** = sample standard deviation

**n** = sample size

In a condition when n becomes** 1,** the square root becomes one as well **(1 = 1)**and the above formula is as follows:

**T = (X – μ) / σ**

**Degree of Freedom for t Score:**

For determining the t score, the df is calculated by the formula:

**df = sample number – 1**

Converting a z score to a t score is just like the way you convert Celsius to Fahrenheit. The basic formula used to convert the z score to a t score is given as follows:

**T = (Z x 10) + 50.**

It is important to keep in mind that:

Both z score and the t score show the deviations from the mean position. But we have to keep in mind that “0” on z score is always considered as a “0” standard deviation from the mean position. For t score the “0” deviation from the mean refers to a mean of 50.

A t score >50 is considered above average. Below 50 is below average. In general, a t score of above 60 means that the score is in the top one-sixth of the distribution; above 63, the top one-tenth. A t score below 40 indicates a lowest one-sixth position; below 37, the bottom one-tenth.

We have a table representing the equivalent z score and t scores as follows:

Z score |
T score |

-5 |
0 |

-4 |
10 |

-3 |
20 |

-2 |
30 |

-1 |
40 |

0 |
50 |

1 |
60 |

2 |
70 |

3 |
80 |

4 |
90 |

5 |
100 |

You can find p value from t value using a t score table against the data you are provided with.

In a t score table,

- You have a df (degree of freedom) column on the most left side and;
- Each row against the individual df level represents the alpha level or significance level.

In this section, we have two tables that are used to determine the t score against the data given in the problem.

**T-Distribution Table (One Tail):**

DF |
A = 0.1 |
0.05 |
0.025 |
0.01 |
0.005 |
0.001 |
0.0005 |

∞ |
ta = 1.282 |
1.645 |
1.960 |
2.326 |
2.576 |
3.091 |
3.291 |

1 |
3.078 |
6.314 |
12.706 |
31.821 |
63.656 |
318.289 |
636.578 |

2 |
1.886 |
2.920 |
4.303 |
6.965 |
9.925 |
22.328 |
31.600 |

3 |
1.638 |
2.353 |
3.182 |
4.541 |
5.841 |
10.214 |
12.924 |

4 |
1.533 |
2.132 |
2.776 |
3.747 |
4.604 |
7.173 |
8.610 |

5 |
1.476 |
2.015 |
2.571 |
3.365 |
4.032 |
5.894 |
6.869 |

6 |
1.440 |
1.943 |
2.447 |
3.143 |
3.707 |
5.208 |
5.959 |

7 |
1.415 |
1.895 |
2.365 |
2.998 |
3.499 |
4.785 |
5.408 |

8 |
1.397 |
1.860 |
2.306 |
2.896 |
3.355 |
4.501 |
5.041 |

9 |
1.383 |
1.833 |
2.262 |
2.821 |
3.250 |
4.297 |
4.781 |

10 |
1.372 |
1.812 |
2.228 |
2.764 |
3.169 |
4.144 |
4.587 |

11 |
1.363 |
1.796 |
2.201 |
2.718 |
3.106 |
4.025 |
4.437 |

12 |
1.356 |
1.782 |
2.179 |
2.681 |
3.055 |
3.930 |
4.318 |

13 |
1.350 |
1.771 |
2.160 |
2.650 |
3.012 |
3.852 |
4.221 |

14 |
1.345 |
1.761 |
2.145 |
2.624 |
2.977 |
3.787 |
4.140 |

15 |
1.341 |
1.753 |
2.131 |
2.602 |
2.947 |
3.733 |
4.073 |

16 |
1.337 |
1.746 |
2.120 |
2.583 |
2.921 |
3.686 |
4.015 |

17 |
1.333 |
1.740 |
2.110 |
2.567 |
2.898 |
3.646 |
3.965 |

18 |
1.330 |
1.734 |
2.101 |
2.552 |
2.878 |
3.610 |
3.922 |

19 |
1.328 |
1.729 |
2.093 |
2.539 |
2.861 |
3.579 |
3.883 |

20 |
1.325 |
1.725 |
2.086 |
2.528 |
2.845 |
3.552 |
3.850 |

21 |
1.323 |
1.721 |
2.080 |
2.518 |
2.831 |
3.527 |
3.819 |

22 |
1.321 |
1.717 |
2.074 |
2.508 |
2.819 |
3.505 |
3.792 |

23 |
1.319 |
1.714 |
2.069 |
2.500 |
2.807 |
3.485 |
3.768 |

24 |
1.318 |
1.711 |
2.064 |
2.492 |
2.797 |
3.467 |
3.745 |

25 |
1.316 |
1.708 |
2.060 |
2.485 |
2.787 |
3.450 |
3.725 |

26 |
1.315 |
1.706 |
2.056 |
2.479 |
2.779 |
3.435 |
3.707 |

27 |
1.314 |
1.703 |
2.052 |
2.473 |
2.771 |
3.421 |
3.689 |

28 |
1.313 |
1.701 |
2.048 |
2.467 |
2.763 |
3.408 |
3.674 |

29 |
1.311 |
1.699 |
2.045 |
2.462 |
2.756 |
3.396 |
3.660 |

30 |
1.310 |
1.697 |
2.042 |
2.457 |
2.750 |
3.385 |
3.646 |

60 |
1.296 |
1.671 |
2.000 |
2.390 |
2.660 |
3.232 |
3.460 |

120 |
1.289 |
1.658 |
1.980 |
2.358 |
2.617 |
3.160 |
3.373 |

1000 |
1.282 |
1.646 |
1.962 |
2.330 |
2.581 |
3.098 |
3.300 |

**T-Distribution Table (Two-Tailed):**

DF |
A = 0.2 |
0.10 |
0.05 |
0.02 |
0.01 |
0.002 |
0.001 |

∞ |
ta = 1.282 |
1.645 |
1.960 |
2.326 |
2.576 |
3.091 |
3.291 |

1 |
3.078 |
6.314 |
12.706 |
31.821 |
63.656 |
318.289 |
636.578 |

2 |
1.886 |
2.920 |
4.303 |
6.965 |
9.925 |
22.328 |
31.600 |

3 |
1.638 |
2.353 |
3.182 |
4.541 |
5.841 |
10.214 |
12.924 |

4 |
1.533 |
2.132 |
2.776 |
3.747 |
4.604 |
7.173 |
8.610 |

5 |
1.476 |
2.015 |
2.571 |
3.365 |
4.032 |
5.894 |
6.869 |

6 |
1.440 |
1.943 |
2.447 |
3.143 |
3.707 |
5.208 |
5.959 |

7 |
1.415 |
1.895 |
2.365 |
2.998 |
3.499 |
4.785 |
5.408 |

8 |
1.397 |
1.860 |
2.306 |
2.896 |
3.355 |
4.501 |
5.041 |

9 |
1.383 |
1.833 |
2.262 |
2.821 |
3.250 |
4.297 |
4.781 |

10 |
1.372 |
1.812 |
2.228 |
2.764 |
3.169 |
4.144 |
4.587 |

11 |
1.363 |
1.796 |
2.201 |
2.718 |
3.106 |
4.025 |
4.437 |

12 |
1.356 |
1.782 |
2.179 |
2.681 |
3.055 |
3.930 |
4.318 |

13 |
1.350 |
1.771 |
2.160 |
2.650 |
3.012 |
3.852 |
4.221 |

14 |
1.345 |
1.761 |
2.145 |
2.624 |
2.977 |
3.787 |
4.140 |

15 |
1.341 |
1.753 |
2.131 |
2.602 |
2.947 |
3.733 |
4.073 |

16 |
1.337 |
1.746 |
2.120 |
2.583 |
2.921 |
3.686 |
4.015 |

17 |
1.333 |
1.740 |
2.110 |
2.567 |
2.898 |
3.646 |
3.965 |

18 |
1.330 |
1.734 |
2.101 |
2.552 |
2.878 |
3.610 |
3.922 |

19 |
1.328 |
1.729 |
2.093 |
2.539 |
2.861 |
3.579 |
3.883 |

20 |
1.325 |
1.725 |
2.086 |
2.528 |
2.845 |
3.552 |
3.850 |

21 |
1.323 |
1.721 |
2.080 |
2.518 |
2.831 |
3.527 |
3.819 |

22 |
1.321 |
1.717 |
2.074 |
2.508 |
2.819 |
3.505 |
3.792 |

23 |
1.319 |
1.714 |
2.069 |
2.500 |
2.807 |
3.485 |
3.768 |

24 |
1.318 |
1.711 |
2.064 |
2.492 |
2.797 |
3.467 |
3.745 |

25 |
1.316 |
1.708 |
2.060 |
2.485 |
2.787 |
3.450 |
3.725 |

26 |
1.315 |
1.706 |
2.056 |
2.479 |
2.779 |
3.435 |
3.707 |

27 |
1.314 |
1.703 |
2.052 |
2.473 |
2.771 |
3.421 |
3.689 |

28 |
1.313 |
1.701 |
2.048 |
2.467 |
2.763 |
3.408 |
3.674 |

29 |
1.311 |
1.699 |
2.045 |
2.462 |
2.756 |
3.396 |
3.660 |

30 |
1.310 |
1.697 |
2.042 |
2.457 |
2.750 |
3.385 |
3.646 |

60 |
1.296 |
1.671 |
2.000 |
2.390 |
2.660 |
3.232 |
3.460 |

120 |
1.289 |
1.658 |
1.980 |
2.358 |
2.617 |
3.160 |
3.373 |

8 |
1.282 |
1.645 |
1.960 |
2.326 |
2.576 |
3.091 |
3.291 |

To understand the proper concept of p value from t statistic, let us solve a couple of examples:

**Example # 01:**

Suppose you performed a two-tailed test and got a t score of 3.25. The sample mean for test is 5 and the level of significance is 1%. calculate p-value from t.

**Solution:**

First of all, we need to determine the degree of freedom as follows:

**df = n – 1 **

**= 5 – 1**

**= 4**

By putting values against all parameters in online p value calculator from t score, we can calculate p value as follows:

**P value = 0.031**

**Example # 02:**

You performed a right tailed test in which A law school claims it’s graduates earn an average of $50 per hour. A sample of 10 graduates is selected and found to have a mean salary of $30 with a sample standard deviation of $50. Assuming the school’s claim is true, how to find p value with test statistics to show that the mean salary of graduates will be no more than $30?

**Solution:**

The given data is:

**x̄ = sample mean = 30**

**μ0 = population mean = 50**

**s = sample standard deviation = 50**

**n = sample size = 10**

Putting all the values in t score formula:

**T = (X – μ) / [ σ/√(n) ]**

**t = 30 – 50 / (50 / √10)**

**t = -20 / 15.822**

**t = -1.264**

Hence, this is our required p value.

For the sample size (n), we can find the degree of freedom as follows:

**df = n – 1 **

**= 10 – 1 **

**= 9**

Now, finding p value from t score will tell you about the probability of the situation that the mean salary of graduates will be no more than $30.

The p value is determined by using our free online p value calculator from t score is:

**P value = 0.88**

P value from test statistics tells you about the probability of the hypothetical situation. You can easily work for the p value using our free online p value calculator from t score.

Let us see what steps you need to follow:

**Input:**

First of all, select either of the following options from the drop down list:

- Two-tailed p value
- Left-tailed p value
- Right-tailed p value

After doing so;

- Put in the value of t score calculated
- Put in the value of significance level
- Put in the value of the degree of freedom
- Click ‘calculate’.

**Output:**

Depending upon the type of test you selected, the calculator calculates either:

- Two-tailed p value
- Left-tailed p value
- Right-tailed p value

Yes, t statistic is a way that tells you how to find p value from test statistics by making a comparison between null hypothesis and alternative hypothesis.

If the absolute t value gets equal to 1.96 or higher than this , we can say that the t value is statistically significant.

A t value of 0 indicates that the results are equal to null hypothesis that we supposed.

Whenever we see negative test statistics, we actually consider a value left to the mean value. From this, we can determine negative t values.

A t-test allows us to relate the average values of the two data sets and determine if they came from the same population. In the field of medical science, the t test is performed to measure the density of bones. An alternative approach is to use free online p value calculator from t score which makes it easier to find p value instantly.

From the source of Wikipedia: Student’s t-distribution, Probability density function, Cumulative distribution function, Sampling distribution, Bayesian inference.

From the source of lumen learning: The t-Test, The t-Distribution, Distribution of a Test Statistic, t-Test for One Sample, Unpaired and Overlapping Two-Sample T-Tests, Independent Samples, Overlapping Samples, Slope of a Regression, Multivariate Testing, Alternatives to the t-Test, Cohen’s d.

From the source of khan academy: Test statistic in a two-sample t test, Conclusion for a two-sample t test using a P-value