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Unformatted text preview: The t Tests Single Sample Dependent Samples Independent Samples From Z to t … In a Z test, you compare your sample to a known population, with a known mean and standard deviation. In real research practice, you often compare two or more groups of scores to each other, without any direct information about populations. Nothing is known about the populations that the samples are supposed to come from. The t Test for a Single Sample The single sample t test is used to compare a single sample to a population with a known mean but an unknown variance. The formula for the t statistic is similar in structure to the Z, except that the t statistic uses estimated standard error . From Z to t … 1 ) ( 2 = ∑ n X X s n s s X = X hyp s X t μ = X hyp X Z σ μ = n X σ σ = N X 2 ) ( μ σ Σ = Note lowercase “s”. ) 1 ( ) ( 2 2 Σ Σ = n n X X n s 2 2 2 ) ( N X X N Σ Σ = σ Why ( n – 1)? When you have scores from a particular group of people and you want to estimate what the variance would be for people in general who are like the ones you have scores from, use ( n 1). To calculate the variance of a sample, when estimating the variance of its population , use ( n 1) in order to provide an unbiased estimate of the population variance. Population of 1, 2, 3 σ 2 = .667 Degrees of Freedom The number you divide by (the number of scores minus 1) to get the estimated population variance is called the degrees of freedom . The degrees of freedom is the number of scores in a sample that are “free to vary”. Degrees of Freedom Imagine a very simple situation in which the individual scores that make up a distribution are 3, 4, 5, 6, and 7. If you are asked to tell what the first score is without having seen it, the best you could do is a wild guess, because the first score could be any number. If you are told the first score (3) and then asked to give the second, it too could be any number. Degrees of Freedom The same is true of the third and fourth scores – each of them has complete “freedom” to vary. But if you know those first four scores (3, 4, 5, and 6) and you know the mean of the distribution (5), then the last score can only be 7. If, instead of the mean and 3, 4, 5, and 6, you were given the mean and 3, 5, 6, and 7, the missing score could only be 4. Degrees of Freedom In the t test, because the known sample mean is used to replace the unknown population mean in calculating the estimated standard deviation, one degree of freedom is lost.degree of freedom is lost....
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This note was uploaded on 01/30/2009 for the course PSYC 60 taught by Professor Ard during the Spring '08 term at UCSD.
 Spring '08
 Ard

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