# disc5 - Notes on week 5 material Topics How the z and...

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Notes on week 5 material

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Topics • How the z- and t-tests are all related • How t-tests are different – Knowledge about population values – z-distribution vs t-distributions (and CVs) – Degrees of freedom, importance of N • The t-tests – Single sample t-test – Independent samples t-test – Repeated measures t-test (next time)
Relationship between tests • The statistical tests we learn about get progressively more complicated – Formula-wise • This is because we know progressively less about the population • …as a result, we have to estimate more population info by using sample info • This takes (math) work

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Relationship between tests • All tests still take the same basic form: • Which means: Observed value of test statistic = Difference between means Measure of average variability you can expect due to chance Observed value of test statistic = Effect of manipulation, chance Estimate of effect of chance
Relationship between tests • Remember that the goal is to factor out chance so you can isolate the effect of your manipulation Observed value of test statistic = Effect of manipulation, chance Estimate of effect of chance

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Relationship between tests • Remember that the goal is to factor out chance so you can isolate the effect of your manipulation Observed value of test statistic = Effect of manipulation, chance Estimate of effect of chance
Relationship between tests • Remember that the goal is to factor out chance so you can isolate the effect of your manipulation Observed value of test statistic = Effect of experimental manipulation only The resulting test statistic is the difference between the means with chance difference FACTORED OUT

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How t-tests are different • With the z-test you know everything about the population (μ, σ ) – Remember: you MUST know σ to do a z-test • With t-tests, you have little (no σ ) or no (no σ , no μ) knowledge about the population • What this means: – You have to do more estimation based on sample values (more math) – You can’t use the z-distribution
The z-distribution • It is a standard normal distribution – You know areas under the curve for proportions, percentages, and CVs • There is only one z-distribution – That is, if you want a critical value for α =.05, 2-tailed test, there is only ONE value you can use • You can only use it if you know σ – Variability of the z-distribution is based on population standard deviation

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The t-distribution(s) • Standardized, like z-distribution – Means it exists in a table for you (A2) • Provides t-values, like z-values – These define proportions, percentages, and CVs
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disc5 - Notes on week 5 material Topics How the z and...

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