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Chapter 9

# Chapter 9

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University of Toronto St. George

Psychology

PSY201H1

Gillian Rowe

Fall

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Chapter 9 Introduction to the t Statistic91 The t Statistic An Alternative to zUsing a sample mean to test hypotheses about an unknown population mean 1 Sample mean M expected more or less to approximate its population mean2 Standard error provides a measure of how well a sample mean approximates the population mean standard error determines how much difference is reasonable to expect between a sample mean M and the population mean OR MM 3 Compare the obtained sample mean M with the hypothesized population meanby computing a zscore test statistic zMM Expected value of the distribution of sample means isthe population mean Goal of the hypothesis test is to determine whether the obtained difference between the data and the hypothesis is significantly greater than would be expected by chanceThe Problem with zScoresA zscore requires we know the value of the population standard deviation or variance which is needed to compute the standard errordont usually know it thoughWhen variability for the population is not known we use the sample variability in its place Introducing the t StatisticUsing sample values we can estimate the standard errorOR MMEstimate standard error by simply substituting sample variance or standard deviation in place of the unknown population valueestimated standard errorsMs OR sMEstimated standard error sMestimate of the real standard error when the value of is Munknown 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 Two reasons for making the shift from standard deviation to variance 21 Sample variance s will provide an accurate and unbiased estimate of the population 2variancemost accurate ways to estimate standard error is to use sample variance to estimate the population variance 2 Estimated standard error t statistictest hypotheses about an unknown pop meanwhen the value ofis unknown The t statistic uses the estimated standard error in the denominatortM sM Degrees of Freedom and the t StatisticDegrees of freedomnumber of scores in a sample that are independent and free to vary There are n1 degrees of freedom for the sampledfn1 22The greater the value of df for a sample the better srepresentsand the better the t statistic approximates the zscore larger the sample better it represents the population

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