Why are t statistics more variable than z-scores?Select one:a.The extra variability is caused by variations in the samplevariance.b.The extra variability is caused by variations in the sample mean.c.None of the other options explains the extra variability for tstatistics.d.The extra variability is caused by variations in the df value.FeedbackThe correct answer is:The extra variability is caused byvariations in the sample variance.
You may want to read these articles first: Show ## T-Score vs. Z-Score: OverviewWatch the video for an overview of when to use a t-score and when to use a z-score: Watch this video on YouTube. Can’t see the video? Click here. A ## T-score vs. z-score: When to use a t scoreThe general rule of thumb for when to use a t score is when your sample: - Has a sample size below 30,
- Has an unknown population standard deviation.
You The above chart is based on (from my experience), the “rule” you’re most likely to find in an elementary statistics class. That said, In real life though, it’s more common just to use the t-distribution as we usually don’t know sigma (SoSci, 1999).
Note the use of the word can in the above quote; The use of the t-distribution is theoretically sound for all sample sizes, but you *can* choose to use the normal for sample above 30. ## T-Score vs. Z-Score: Z-scoreTechnically, z-scores are a conversion of individual scores into a standard form. The conversion allows you to more easily compare different data; it is based on your knowledge about the The z-score is calculated using the formula: z = (X-μ)/σ Where:
- σ is the population standard deviation and
- μ is the population mean.
The z-score formula doesn’t say anything about sample size; The rule of thumb applies that your sample size should be above 30 to use it. ## T-Score vs. Z-Score: T-scoreLike z-scores, t-scores are also a conversion of individual scores into a standard form. However, t-scores are used T = (X – μ) / [ s/√(n) ].Where: - s is the standard deviation of the sample.
If you have a larger sample (over 30), the t-distribution and z-distribution look pretty much the same. Therefore, you can use either. That said, if you know σ, it doesn’t make much sense to use a sample estimate instead of the “real thing”, so just substitute σ into the equation in place of s: T = (X – μ) / [ σ/√(n) ].This makes the equation identical to the one for the z-score; the only difference is you’re looking up the result in the T table, not the Z-table. For sample sizes over 30, you’ll get the same result. ## ReferencesEveritt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of Statistics, Cambridge University Press.
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