What are some examples of T-scores in statistics?

What are some examples of T-scores in statistics?

A T-score is a type of standard score that indicates how many standard deviations an element is from the mean. For example, if a student scores 85 on a test where the mean is 75 and the standard deviation is 5, the T-score would be calculated as follows: T = (85 - 75) / 5 = 2. This means the student's score is 2 standard deviations above the mean.

Can you give me another example?

Sure! Let's say a researcher measures the heights of a group of people and finds the mean height is 170 cm with a standard deviation of 10 cm. If one person is 180 cm tall, their T-score would be T = (180 - 170) / 10 = 1. This indicates that the person's height is 1 standard deviation above the mean.

How do T-scores differ from Z-scores?

Great question! T-scores are used when the sample size is small and the population standard deviation is unknown, while Z-scores are used for larger samples or when the population standard deviation is known. T-scores have a different distribution, which accounts for the additional uncertainty in smaller samples.

What is the significance of T-scores in hypothesis testing?

T-scores are crucial in hypothesis testing as they help determine whether to reject the null hypothesis. A higher absolute T-score indicates a greater difference from the null hypothesis, which can lead to a statistically significant result.