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Arizona State University *

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Statistics

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Apr 29, 2024

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docx

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T(EA) for Two: Tests between the means of different groups Determining Correct Statistic:  Most statistical tests have underlying assumptions. o T-test assumes equal variability in each group (homogeneity of variance). o Smaller sample sizes may pose challenges if this assumption is violated. One-Sample Tests:  Two common inferential tests: o One-sample Z test o One-sample t test. o Both compare the mean score of a sample with another score (often the population mean).  Despite using different calculations and tables, they yield similar conclusions. Independent samples:  If the values in one sample reveal no information about or are unrelated to those of the other sample, then the samples are independent Dependent samples:  If the values in one sample affect or are related to the values in the other sample, then the samples are dependent Equal VS Unequal Variance  For independent samples, you have to specify variance of the two groups o Can run specialized test (Welch t-test) to examine variances o As a general rule, you can assume equal variance if the ratio of the sample variances (s 1 2 /s 2 2 ) is between 0.5 and 2 o i.e. the variances of the two samples are no more than double each other

Paired two sample for means two-sample assuming equal/unequal variance

Calculating two-sample T-Test: Independent Samples – by hand

Example for two-sample t-test: independent samples Researchers wish to know which treatment protocol is more effective at helping Alzheimer’s patients remember words. They divide a group of Alzheimer’s patients into two groups. Group 1 was taught using visuals, and Group 2 was taught using visuals and intense verbal rehearsal.

1. State the null and alternative hypothesis: a. The null hypothesis: the mean of group one will equal the mean of group two. i. H 0 : 𝑥 = 𝑥 b. Alternative/research hypothesis: the mean of group one will be different than the mean of group two-nondirectional hypothesis. i. H 1 : 𝑥 ≠ 𝑥 2. State the test statistic formula: Unequal t-test because we know the standard deviation and our sample is 30 or less. The standard deviations are not equal from the data provided a. 3. State the level of significance: .05 a. for this class our default level of significance is .05, unless stated otherwise. 4. Compute the test statistic 5. Determine the critical value or p-value 6. Determine the statistical conclusion 7. State the experimental conclusion Limitations:  Only evaluate means o Can not make conclusions about individual scores  Affected by sample size o Results of analyses from different studies can not be compared Computing the T Test Statistic The formula for computing the t value for the t test for independent means. All these symbols really just provide two important values to computing the T-Test Statistic. First is the difference between the two means makes up the numerator, and the denominator (top of the equation) makes up the amount of variance within and between each of the two groups. 1. State the null and research hypotheses:

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