What’s the Difference Between a T Score and a Z Score?
You may have heard about T and Z scores if you’ve ever taken or scored a standardized test. These two numbers seem very similar, but they’re quite different.
The main difference between the two is that Z scores are based on your sample data’s mean and standard deviation.
In contrast, T scores are based on the mean and standard deviation of the entire population of test-takers who have taken the same test as you did. So which kind of number do you use? And why do you need to use them at all?
What is the T Score?
An IQ test score is often expressed in T scores—the number of standard deviations from 100 that an individual’s score falls.
A T score can range from -3 to +3; most people fall within one standard deviation, which ranges from -1.5 to +1.5, so half of the IQ scores fall between 85 and 115.
As you go further away from 100, you move toward either end of two standard deviations (T scores above 145 or below 70), making it more likely that your true intelligence (as measured by a full battery of tests) differs significantly from your performance on an IQ test.
How to Calculate the T Score?
To calculate your t score, take your test score minus your reference score, then divide it by 1.96 (or subtract 1.96 from it).
If you are testing with a computerized version of either test, enter your raw score and percentile rank into an INVT calculator to see what you get.
The result will be between -3.00 and 3.00 (for verbal) or -3.40 to 3.40 (for math), so feel free to round up or down as necessary if you don’t have time for subtraction or decimal division—there is no wrong answer after all!
What is the Z Score?
The Z score indicates how far an observation deviates from the mean by standard deviation. For example, if your average daily calorie intake is 2,300 calories per day, that means that 50% of people who kept track of their diets were under 2,300 calories per day, and 50% were over 2,300 calories per day.
If you eat 3,000 calories one day, you are one standard deviation above your mean; another way to put it is that 68% of people who kept track of their diets ate less than 3,000 calories in a single day.
How to calculate the Z Score?
The Z score can be calculated by subtracting the T score from 50 (or 10000) to find a percentile rank. For example, if you have an ACT T score of 28 and your desired percentile rank is 65%, you must get a Z score of 35.
The formula is [T – 50] / [10 x (desired percentile rank – 50)]. If you have an ACT Math section with a T score of 38 and an ACT English section with a T score of 29, then you’d do [38-50] / [10*(65-50)] = 0.44, which means that your combined Math/English total needs to be 44 or higher to place in that 65th percentile.
What is the Use of the T Score and Z Score?
Both scores measure how many standard deviations below or above an average person of your age you are. However, they use different measurements to determine that number:
A t score is based on test results (like your SAT), while a z score is based on your raw data (like how tall you are).
One may not necessarily be better than another because of this; they just differ. So, what do these scores mean for you—and how can you use them to understand your academic performance?
Let’s dive in! T Score vs. Z Score: What Are They & How Do I Calculate Them? T scores are used in testing situations like standardized tests such as the SAT.
What Are the Different Types of T Scores and Z Scores?
T scores are based on a normal distribution (bell curve), meaning they assume that each test-taker has an equal chance of scoring at any point on the curve.
The standard deviation is used to calculate all of your individual T scores and your standard score. Z scores are based on an ideal bell curve, where every person is exactly average: no one is any smarter or dumber than anyone else, but they all have different IQs.
You should use z-scores to be more specific about someone’s relative intelligence than other test-takers.
To determine if someone is smarter than average, you can use both scores: take their T score and subtract it from 100.
Should I use T-score or z score?
When taking a standardized test, one of your scores will be reported as either a T or z score. And if you ever wonder which is which, here’s what you need to know: A T score is essentially a raw test score—the number of questions you got right out of how many total questions on that section.
For example, if there were 40 multiple-choice questions on math and you got 32 of them right, your math T score would be 80% (32 out of 40).
A z-score is much more complicated than that—it involves your raw test scores and other statistics like how much harder or easier each section was compared to the average.
Is the T stat the same as the Z score?
In statistics, if you want to compare two datasets, you need to use a test statistic. The two most common test statistics are the T and Z scores.
This can be unclear for those new to these terms because they may sound similar. These two values, however, vary markedly in practice and are, therefore, helpful in various contexts.
As one can see, there is not much difference between t-scores and z-scores when comparing data. But, depending on your desired outcome and dataset, you should choose whether you want to calculate t-scores or z-scores for your research. To make sure that you’re using valid statistical methods for your research needs, always consult with an expert in statistics! Sometimes, t-score calculators like (find one) are available to help you easily convert raw data into usable information. Even if it’s simply a matter of switching from t-scores to z-scores or vice versa, statistics experts can help ensure that it is done correctly.
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