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# T-Statistic Psyc-21621

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This 3 page Class Notes was uploaded by Amy Turk on Wednesday April 27, 2016. The Class Notes belongs to Psyc-21621 at Kent State University taught by Dr. Gordon in Spring 2016. Since its upload, it has received 5 views. For similar materials see Quantitative Methods Psych I in Psychlogy at Kent State University.

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Date Created: 04/27/16

PSYCH STATS POWERPOINT 9 ● t statistic ● when we set a = .05, this result will only occur at random 5% of the time ○ we are 95% sure our result didn’t occur by chance ● df = (n-1) ● standard error indicates the variability in M ● we use z-scores to test our hypothesis ● with t-statistics, we don’t have certain information ● confidence intervals = give us an idea of how well our numbers are at estimating the values ● we rarely know the SD ○ we use “s” to estimate the standard deviation ■ the sample standard deviation has sampling variability ● t-statistic = used to test hypotheses about an unknown population mean when the value of SD is unknown ○ when we do hypothesis testing we hypothesize a value of mew ● because we will be working with samples, we can substitute the values ● SD = square root of the variance ● we’re going to focus on formulas using variance ● degrees of freedom = describes the number of scores in a sample that are independent and free to vary ○ the greater the df, the better the sample variance represents the population variance ■ the better the t-statistic approximates the z- score ● the t-distribution will approximate a normal curve ○ how well it approximates depends on the df ● the greater the sample size the better ● the t-distribution has more variability than the z-distribution, especially when n is small ○ more flat and spread out William Sealy Gosset ● born in June 13, 1876 ● attended winchester college, and new college, Oxford ● graduated in 1899 and took employment at a brewery in Dublin ● Gosset was interested in the selection of the best varieties of barley ● he worked with Karl Peterson (a famous statistician) who did not find the problem interesting ● Gossett invented the t-distribution by working with random numbers ○ by far the most important advancement in statistical science that has ever occurred ● published his paper under a pseudonym ○ “a student of statistic” ■ “student’s t” ● to evaluate the t statistic from a hypothesis test, you must select an alpha level, find the value of df for the t statistic, and consult the t distribution table ● if the obtained t statistic is larger than the critical value from the table, you can reject the null hypothesis ● the critical value is the “cut-off” point at which your sample is statistically significant ○ using the t-table to find your critical value Step 1 ● determine the alpha level ● if alpha = .05, we know we will be looking for a proportion in the tain of .05 ● if alpha = .01, we know we will be looking for a proportion in the tail of .01 Step 2 ● determine the direction of the hypothesis ● if the hypothesis is one-sided, use the first row at the top of the table ● if the hypothesis is two sided, use the second row at the top of the table Step 3 ● determine the degrees of freedom and find it on the left side of the table ● df = n-1 Step 4 ● based on the df and the alpha level, find the corresponding critical value ● this is the value we need to exceed to have a significant finding ● one-sided = t will need to exceed this value in that direction (either positive or negative) ● two-sided = t will need to exceed the value in either direction Hypothesis testing with T ● the population must be normal ● the values in our sample must be independent ○ no relationship between observations ○ the same person cannot be included twice ● whenever a sample is obtained from a population, you expect to find error between M and mew ○ sampling error ● the goal of a hypothesis test is to evaluate the significance of this observed error ● the hypothesis test attempts to decide between the following ○ is it reasonable that the discrepancy between M and mew is simply due to sampling error and not the treatment effect? ○ is the discrepancy between M and mew more than would be expected from sampling error alone? ■ is the sample mean significantly different from the population? ● reject or fail to reject the null hypothesis based on alpha and df ● extreme t-values (large ratio values) have lower probability = reject ● small t-values (ration values closer to zero) have higher probabilities = fail to reject ● use cut-off t-scores from table B.2 ● the larger the value, the less probable it is to occur in the population ● extreme t-values have lower probability ○ reject ● small t-values have higher probability ○ fail to reject ● the t-distribution is more dependent on the degrees of freedom Chapter 10 ● 2 different t-tests ○ between subjects ■ independent measures ■ men vs. women ■ drug vs. no drug ■ different groups or people are compared ○ within-subjects ■ repeated measures ■ same people are compared ■ ex. before and after test ■ generally when you manipulate something ● ex. compare happiness before and after moving to Virginia

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