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In educational assessment, T-score is a standard score Z shifted and scaled to have a mean of 50 and a standard deviation of 10. [14] [15] [16] In bone density measurements, the T-score is the standard score of the measurement compared to the population of healthy 30-year-old adults, and has the usual mean of 0 and standard deviation of 1. [17]
Difference between Z-test and t-test: Z-test is used when sample size is large (n>50), or the population variance is known. t-test is used when sample size is small (n<50) and population variance is unknown. There is no universal constant at which the sample size is generally considered large enough to justify use of the plug-in test.
Most frequently, t statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals. The key property of the t statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on the population parameters, and thus it can be used regardless of what these ...
From the t-test, the difference between the group means is 6-2=4. From the regression, the slope is also 4 indicating that a 1-unit change in drug dose (from 0 to 1) gives a 4-unit change in mean word recall (from 2 to 6). The t-test p-value for the difference in means, and the regression p-value for the slope, are both 0.00805. The methods ...
Negative scores indicate lower bone density, and positive scores indicate higher. Less than 0.5% of patients who underwent DXA-scanning were found to have a T- or Z-score of more than +4.0, often the cause of an unusually high bone mass (HBM) and associated with mild skeletal dysplasia and the inability to float in water. [9]
For the statistic t, with ν degrees of freedom, A(t | ν) is the probability that t would be less than the observed value if the two means were the same (provided that the smaller mean is subtracted from the larger, so that t ≥ 0). It can be easily calculated from the cumulative distribution function F ν (t) of the t distribution:
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Z tables use at least three different conventions: Cumulative from mean gives a probability that a statistic is between 0 (mean) and Z. Example: Prob(0 ≤ Z ≤ 0.69) = 0.2549. Cumulative gives a probability that a statistic is less than Z. This equates to the area of the distribution below Z. Example: Prob(Z ≤ 0.69) = 0.7549. Complementary ...