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SE stands for ''standard error'' in statistics. Thanx Sylvia It is the same as the standard deviation of a sampling distribution, such as the sampling distribution of the mean.
11.51% of the distribution.
Sampling distribution in statistics works by providing the probability distribution of a statistic based on a random sample. An example of this is figuring out the probability of running out of water on a camping trip.
z=x-mean / sd
Not necessarily. Inferential statistics are statistics which are used in making inferences about some distribution. The only requirement is that they are based only on the set of observed values.
Each different t-distribution is defined by which of the following? @Answer found in section 4.3 The One-sample t-Test, in Statistics for Managers
SE stands for ''standard error'' in statistics. Thanx Sylvia It is the same as the standard deviation of a sampling distribution, such as the sampling distribution of the mean.
If X is Normally distributed with mean 65 seconds and sd = 0.8 seconds, then Z = (X - 65)/0.8 has a Standard Normal distribution; that is, Z has a N(0, 1) distribution. The cumulative distribution for Z is easily available - on the net and in any basiic book on statistics. To get to the cumulative dirtribution function of X all you need is to use the transformation X = 0.8*Z + 65.
In statistics, the z-scale results from a transformation by which a Gaussian (Normal) distribution with any mean and variance is converted to a standard form: the z-score. This is tabulated so that inferences may be drawn from observed data.
Why we prefer Normal Distribution over the other distributions in Statistics
Tables of the cumulative probability distribution of the standard normal distribution (mean = 0, variance = 1) are readily available. Almost all textbooks on statistics will contain one and there are several sources on the net. For each value of z, the table gives Φ(z) = prob(Z < z). The tables usually gives value of z in steps of 0.01 for z ≥ 0. For a particular value of z, the height of the probability density function is approximately 100*[Φ(z+0.01) - Φ(z)]. As mentioned above, the tables give figures for z ≥ 0. For z < 0 you simply use the symmetry of the normal distribution.
It is called a normal distribution.
A z distribution allows you to standardize different scales for comparison.
example of symmetrical distribution
It is the so-called "half-normal distribution." Specifically, let X be a standard normal variate with cumulative distribution function F(z). Then its cumulative distribution function G(z) is given by Prob(|X| < z) = Prob(-z < X < z) = Prob(X < z) - Prob(X < -z) = F(z) - F(-z). Its probability distribution function g(z), z >= 0, therefore equals g(z) = Derivative of (F(z) - F(-z)) = f(z) + f(-z) {by the Chain Rule} = 2f(z) because of the symmetry of f with respect to zero. In other words, the probability distribution function is zero for negative values (they cannot be absolute values of anything) and otherwise is exactly twice the distribution of the standard normal.
11.51% of the distribution.
If you have a variable X distributed with mean m and standard deviation s, then the z-score is (x - m)/s. If X is normally distributed, or is the mean of a random sample then Z has a Standard Normal distribution: that is, a Gaussian distribution with mean 0 and variance 1. The probability density function of Z is tabulated so that you can check the probability of observing a value as much or more extreme.