P Value from T Score Calculator

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.

What is T Score in 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.

T Score Formula:

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

T Score From Z Score:

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:

How to Read a T Score Table:

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):

T-Distribution Table (Two-Tailed):

How to Calculate P Value From T?

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

How P Value Calculator From T Score Works?

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

FAQ’s:

Can you calculate p value from t statistic?

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.

What is meant by statistically significant t value?

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

What does a t value of 0 indicates?

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

Can you calculate negative t values?

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

Conclusion:

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.

Reference:

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