One Sided T Test Calculator

Calculator

Sample label

Sample mean

Sample standard deviation

Sample size

Hypothesized mean

Alpha level

Alternative hypothesis

Decimal places

Output options

Raw sample data

Raw data overrides summary inputs when at least two values are entered.

Formula Used

The one sample one sided t test uses the sample mean, hypothesized mean, sample standard deviation, and sample size.

t = (x̄ - μ0) / (s / √n)

df = n - 1

Right tailed p value = P(Tdf ≥ t)

Left tailed p value = P(Tdf ≤ t)

Cohen's d = (x̄ - μ0) / s

For a right tailed test, the calculator reports a lower one sided confidence bound. For a left tailed test, it reports an upper bound.

How to Use This Calculator

Enter raw observations, or enter summary statistics.
Type the hypothesized population mean.
Select a right tailed or left tailed alternative.
Enter the alpha level, such as 0.05.
Choose decimal places for the final output.
Press Calculate to view the result above the form.
Use CSV or PDF buttons to save the calculation.

Example Data Table

Example	Tail	Sample Data	μ0	Alpha	Mean	SD	t	p Value	Decision
Quality score	Right	52, 55, 49, 58, 54, 57, 56	50	0.05	54.4286	3.1015	3.7779	0.0046	Reject H0
Processing time	Left	18, 17, 19, 16, 18, 15, 17	20	0.05	17.1429	1.3452	-5.6191	0.0007	Reject H0

One Sided T Test Guide

A one sided t test checks whether a sample mean is higher or lower than a claimed population mean. It is used when the research question has a clear direction before the data is reviewed. The calculator accepts summary values or raw observations. It then finds the sample size, mean, standard deviation, standard error, test statistic, degrees of freedom, p value, critical value, effect size, and a one sided confidence bound.

When To Use It

Use this test for one sample data when the population standard deviation is unknown. The data should be numerical. Observations should be independent. The distribution should be close to normal, especially for small samples. Larger samples are more flexible because the sampling distribution becomes more stable.

Choosing The Tail

Select a right tailed test when the alternative claim says the mean is greater than the hypothesized value. Select a left tailed test when the claim says the mean is less than that value. The tail choice changes the p value and rejection region. It should not be changed after seeing the result.

Reading The Result

The t statistic measures how many standard errors separate the sample mean from the hypothesized mean. A large positive t supports a greater than claim. A large negative t supports a less than claim. The p value gives the probability of getting evidence this extreme, assuming the null claim is true. If the p value is less than or equal to alpha, reject the null claim.

Useful Output

The calculator also reports Cohen's d. This effect size shows the difference in standard deviation units. It helps judge practical strength, not only statistical significance. The one sided confidence bound gives a directional estimate for the population mean. A right tailed test gives a lower bound. A left tailed test gives an upper bound. Export buttons help save the result for reports, audits, homework, or repeat analysis.

Good Practice

Enter raw data when possible. It reduces rounding error. Check outliers before trusting the conclusion. Use a reasonable alpha level, such as 0.05, unless your field requires another value. Always report the tail direction, t statistic, degrees of freedom, p value, and decision together in clear language.

FAQs

What is a one sided t test?

It tests whether a sample mean is greater than or less than a hypothesized population mean. It uses sample variation because the population standard deviation is unknown.

When should I choose a right tailed test?

Choose it when your alternative claim says the population mean is greater than the hypothesized value. This direction should be selected before analyzing the data.

When should I choose a left tailed test?

Choose it when your alternative claim says the population mean is less than the hypothesized value. It places the rejection region in the left tail.

Can I enter raw data?

Yes. Enter values separated by commas, spaces, semicolons, or line breaks. Raw data overrides the summary fields when two or more values are supplied.

What does the p value mean?

The p value shows how unusual the sample result is under the null hypothesis. A smaller p value gives stronger evidence against the null claim.

What alpha level should I use?

Many studies use 0.05. Some fields use stricter levels, such as 0.01. Choose alpha before testing to avoid biased decisions.

What assumptions are required?

Data should be numerical, independent, and reasonably normal for small samples. With larger samples, the test is usually more stable.

What is Cohen's d?

Cohen's d is an effect size. It expresses the mean difference in sample standard deviation units, helping you judge practical importance.