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Statistical Significance What is Statistical Significance? How Do We Know Whether a Result is Statistically Significant? How Do We Know Whether a Result is Statistically Significant? Significance as a Probability Game What is a Sampling Distribution?

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What is Statistical Significance? Statistical significance is a technical decision made using inferential statistics. We say that a result is statistically significant if our inferential statistic indicates that we reject the Null Hypothesis.

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How Do We Know Whether a Result is Statistically Significant? Test the Null Hypothesis using an inferential statistic. The result of the statistical test indicates a probability. If the probability is lower than our criterion significance level, we reject the Null, meaning that the result is significant.

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Determining Significance The Null Hypothesis (H o ) states that there is no difference, effect, or correlation in the population H o is assumed to be true unless there is enough evidence to reject it. Burden of proof on the researcher The researcher’s hypothesis (Alternative Hypothesis, H A ) is only tested indirectly

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Determining Significance How strong does the evidence have to be to reject the Null? The researcher must set a criterion. This is the significance level, or alpha ( ). The conventional alpha level is.05. We are conservative about rejecting Ho.

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Determining Significance When testing for significance, we calculate a test statistic. The test statistic allows us to determine the probability of obtaining our results under the assumption that H o is true. If this probability is small enough, then H o is probably not true, so we should reject it.

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Determining Significance If the probability is lower than our significance level, we Reject Ho (p <.05). If the probability is not lower than our significance level, we Fail to Reject Ho (p >.05). Ho is never “accepted” or “proven.”

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Significance as a Probability Game There are four possible outcomes in significance test, based on two dimensions: – The researcher’s decision about Ho. – Whether Ho is really true or false. The probability of each outcome can be determined.

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Ho true Ho false TRUE STATE OF THE WORLD DECISION RejectHo Fail to Reject Ho Type I error Correct 1 - Correct 1 - (power) Type II error (beta)

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Statistics as a Probability Game is set by the researcher 1- depends on

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Statistics as a Probability Game Power is increased by: – higher alpha – larger sample – lower variability – larger effect size Anything that increases power decreases beta

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What is a Sampling Distribution? A hypothetical frequency distribution of sample statistics from an infinite number of samples. Allows us to make probability judgments about the likelihood of obtaining a particular result.

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Imagining a Sampling Distribution 1.Take a random sample. 2.Compute the mean. 3.Take another random sample and compute the mean. 4.Do this an infinite number of times. 5.Put the resulting sample means in a frequency distribution.

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Nice Things About Sampling Distributions 1. The mean is the hypothesized population mean. 2. The standard deviation can be calculated (standard error). 3. The shape is usually normal.

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Central Limits Theorem The sampling distribution becomes more normal as the sample size increases. With a sample size of 30 or more, the sampling distribution becomes very close to exactly normal.

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Why These Are “Nice” Things If you know the and of a distribution, you can compute z-scores. In a normal distribution, you can look up the proportion of scores above or below any z score. For any sample mean in the sampling distribution, we can find the proportion of sample means above or below it.

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Making Inferences There are three distributions used when we make an inference: – sample distribution – sampling distribution – population distribution The sampling distribution is the “bridge” from the sample to the population.

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