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Chapter 9

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PSYC 1010

nd Chapter 9- The Single-Sample t Test & Paired-Samples t Test March 2 , 2013 The t Distributions - Three types of t test: 1) Single-sample t test- used when comparing a sample mean to a population mean but do not know the population standard deviation 2) Paired-samples t test- used when comparing two samples and every participant is in both samples- within groups design 3) Independent-samples t test- used when comparing two samples and every participant is in only one sample- between groups design - The t test tells us how confident we can be that what we have learned from our samples generalizes to the larger populations - The t distributions are used when we don’t have enough information to use the z distribution, used when sampling requires us to estimate the population standard deviation form the sample standard deviation or when we compare two samples to one another - Estimating population standard deviation from the sample  Use the standard deviation of the sample data to estimate the standard deviation of the entire population  √  We subtract 1 from the sample size in the denominator to correct for the probability that the sample standard deviation slightly underestimates the actual standard deviation in the population  Two steps to calculate the estimated standard deviation for the population: 1) Calculate the sample mean 2) Use this sample mean in the corrected formula (above) for the standard deviation - Calculating the standard error for the t statistic  We need to make our spread smaller to reflect the fact that a distribution of means is less variable than a distribution of scores  √ - Using standard error to calculate the z statistic  T statistic- indicates the distance of a sample mean from a population mean in terms of the standard error  Formula for the t statistic for a distribution of means:  Single Sample t Test - A hypothesis test in which we compare data from one sample to a population for which we know the mean but not the standard deviation - T Table and Degrees of Freedom  Degrees of freedom- the number of scores that are free to vary when estimating a population parameter from a sample  Formula for degrees of freedom for a single-sample t test:  df=N-1  When conducting hypothesis testing, we use the t table to determine critical values for a given p level, based on the degrees of freedom and whether the test is one or two tailed  As sample size increases, the t distributions more and more closely approximate the z distribution - Six steps of the Single-Sample t Test: 1) Identify the populations, distribution, and assumptions 2) State the null and research hypotheses 3) Determine the characteristics of the comparison distribution
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