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Chapter 9

PSYC202 Chapter 9 Into to t Statistic.docx

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PSYC 202
Ronald R Holden

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 PSYC202 Chapter 9 : Introduction to the   t    Statist c The t Statistic: An Alternative to Z ­ Problem with Z­scores  ▯require more information than is usually available o Population standard deviation usually not known ­ When population variabili2y not known, we use the sample variability in its place ­ Sample variance = S  = SS = SS       n­1   df ­ Sample Standard Deviation: S = same as above but  all square rooted ­ Estimated Standard Error: an estimate of the real standard error σ  when the M value of σ is unknown. It is computed from the sample variance or sample  standard deviation and provides an estimate of the standard distance between a  sample mean M and the population mean μ 2 o S =MS        or      √S            √n                 √n ­ 2 reasons to shift from standard deviation to variance: o Variance is unbiased. Sample variance (s ) will provide an accurate  2 estimate of the population variance (σ ) ­ T­statistic: used to test hypotheses about an unknown population mean μ when  the value of σ is unknown. Same structure as z­score formula, except uses S   M instead of σ o t=  M­   μ            MS ­ Degrees of Freedom: number of scores in a sample that are independent and free  to vary. Because the sample mean places a restriction on the value of one score in  the sample, there are n­1 degrees of freedom for the sample. 2 2 o The greater the value of df, the better S represents σ , and the better t  approximates the z­score. Larger sample = more accurate. ­ t-distribution ▯ distribution of t-scores similar to z-scores – both normal. How normal the distribution is depends on the degrees of freedom. Higher sample = higher degrees of freedom (n-1) = closer to normal distribution o Bell-shaped, symmetrical, mean = 0 o T-distribution has more variability than z, and tends to be flatter & more spread out ▯ because denominator of t-equation (S ) changes from sample
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