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One_sample_ttest 15 - More about Hypothesis Testing Testing...

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More about Hypothesis Testing Testing the Null Differences between Populations
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The Null Hypothesis We have the information to figure the probability of getting the result if there was NO difference between the populations. 5% probability of getting the result if No Program Kids are the same as Program Kids
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The Null Hypothesis What is the probability of getting our results if there is NO effect ? 5% probability of getting the result if No Program Kids are the same as Program Kids (i.e, that there is NO effect of the program)
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The Null Hypothesis We know about the situation if there is NO effect. We know about kids NOT in the program. If NO effect, then we also know about kids in the program. Known population: No Program Kids Unknown population: Program Kids If NO effect, these populations are the same.
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The Null Hypothesis We are actually testing the hypothesis that there is NO effect of the program. This is the NULL hypothesis. We actually test the null hypothesis. Called Null Hypothesis Significance Testing (NHST)
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The Research Hypothesis The research hypothesis is the one the researcher is usually interested in. The research hypothesis is that there IS an effect.
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The Null and Research Hypotheses Research Hypothesis – there IS an effect. The reading program works. Symbol for research hypothesis is H 1 Null Hypothesis – there is NOT an effect. The reading program does NOT work. 0
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Hypotheses and Populations The hypotheses are usually stated in terms of the populations of interest and their means. Pop 1 = No Program Kids Mean of Pop 1 = μ 1 Pop 2 = Program Kids Mean of Pop 2 = μ 2 Research Hypothesis: The Program Kids will have higher reading scores than the NO Program Kids. H 1 : μ 1 < μ 2 Null Hypothesis: The Program Kids will have scores that are lower or the same as the No Program Kids. H 0 : μ 1 >= μ 2
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The population you compare your sample to Known Population Comparison (Known) Population
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Population of Interest (Unknown) The one your sample came from Unknown population
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Both populations Not usually this (no overlap) Known Pop Unknown Pop
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Usually some overlap Known Pop Unknown Pop
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Distribution of Means Two Distributions of Means One from known population All of the samples in this distribution are the same sample size (which is the same size as our sample) One from unknown population All of the samples in this distribution are the same sample size (same as the size of our sample) Population unknown, so only have a sample – need to estimate the population from the sample. Compare this sample to the distribution of means from known populations
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Two Distributions of Sample Means (sample size the same in both) SCORE -4 -2 0 2 4 0.0 0.1 0.2 0.3 0.4 SCORE -4 -2 0 2 4 0.0 0.1 0.2 0.3 0.4 No Program Kids Program Kids NO overlap!
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