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Psyc 60 t Tests

Psyc 60 t Tests - The t Tests Single Sample Dependent...

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    The  t  Tests Single Sample Dependent Samples Independent Samples
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    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.
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    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  statistic is similar in  structure to the Z, except that the  t   statistic uses  estimated standard error .
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    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
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    Why ( – 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
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    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”.
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    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.
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    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.
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    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.
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