If you lack statistical understanding, you may feel trapped by many statistical issues. T score versus z score are two confusing terms.

However, I have covered everything pertaining to t and z scores. Also, I compared t score against z score in detail. This will help you understand the t and z scores. Begin with the details.

What is t?

T score is the transformation of unstructured data into standard scores. Considering the sample standard deviation and sample mean while converting.

If you don’t have population data, you can use sample data to compute sample SD and mean.

Which z score?

Z score is the transformation of unstructured data into standard scores. It takes into account the population standard deviation and sample mean.

It can be utilized when you have all the test data.

Is there a formula for calculating the t and z scores?

Yes!

The t score is calculated as follows:

Where,

0 = mean population

sample mean

SAMPLE SIZE n

s = sample SD

If the sample observation contains only one item, the denominator’s square root will be 1. So the t score formula is:

Let’s see an example:

A institution boasts that female graduates earn on average $300/hour. It is based on a sample of 15 graduates, with a mean of $280 and a T-score of university women graduation pay

Solution:

Written as follows:

+20/(50/13) -1.549 (280–300)

The z score is calculated as follows:

Where,

(Mean population)

- X Equals raw data

- = SD of the population

Let’s see an example:

Assume a test score of 180 with a mean of 140 and an SD of 20. Find the z score.

Solution:

z = (x –)/

180 – 140 = 2

That is, how many SDs the actual score is. Your z score is 2 SD above the mean. Now let’s compare the t and z scores.

t score vs z score

T score Z score

Data standardization

It is used to standardize Sample SD and Data.

It is used to standardize population SD and statistics.

std dev

The t score standard deviation is always 10.

The z score standard deviation is always 1.

Suffixes

Use a T score when the sample size is less than 30 or the population set is unknown.

When the Population set is known or exceeds 30, use a Z score.

The mean is always 50.

The mean is always zero.

Result

The t score is never negative.

The z score is usually negative.

Range

It is between 20 and 80.

It is -3 to 3.

Distribution

T score is a subset of T.

A Z score is a Z distribution.

Preference

T score is preferred for higher range values, however it has inherent size limitations.

Z score is less preferred due to its data support.

Use with size increase

Its utility decreases with size.

The Z score can be utilized with a size change.

Is there a reason to employ t or z scores?

Yes! There is also a usage rule.

The t score is utilized when:

- unclear population SD,

- less than 30 samples

The z score is utilized when:

- std dev

If the sample size exceeds 30.

This is an example of an experienced-based chart that you may have used in elementary statistics. In practice, the t score is employed with the t distribution.

If there are more than 30 measurements in the sample, the normal distribution can be used.

Where can z and t scores be used?

You can utilize both t and z scores after you grasp their differences. In practice, the Z score is used to assess a company’s risk of insolvency. Also, in biostatistics, z score is used to analyze nutritional data, especially for children.

The t score is used to determine fracture risk, bone loss, mineral density, and normal bone density. The t-score is also employed when the statistician does not know the population SD and must estimate using the sample.

Remember:

T and z scores both describe standard deviation. When “0” of the z score is 0 SD from the mean, then “50” of the t score is the same as “0”.

Because the t score uses 50 and the z score uses 0.

T scores above 60 are in the top 1/6 of the distribution. If it’s over 63, it’s the top 10%.

When the t score is below 40, it describes the 1/6th position. If it’s below 37, the distribution is 1/10th.

Conclusion

When converting between population standard deviation and mean, the user should use a z score. When converting between sample standard scores and sample means, the user should utilize a t score.

Everybody’s got a purpose for them! So, its application and use can be tailored to the statisticians’ needs. I’ve discussed the distinctions between t and z scores above so you can simply pick which to use.

If you have any questions, please ask. Comment your questions below and I will do my best to answer them.

Questions & Answers

When to utilize T scores

When using the t score, two points must be considered:

When the population standard deviation is unknown.

When the sample is under 30.

What is the Z score?

A Z-score indicates how many SD an analysis deviates from the mean. OR IT SIMPLIFIES OR RESCALES YOUR DATA A Z-score helps locate all observations inside a distribution.

Why is z score vital?

The z score helps statisticians because it:

(a) determines the likelihood of a certain score appearing within the normal distribution

,

This enables them to compare several normal distribution scores.