Topic_7.0___Statistical_Inference___Significance_Tests

Topic_7.0___Statistical_Inference___Significance_Tests -...

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Statistical Inference – Significance Tests Ash Genaidy
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Introduction A common goal of many engineering investigations is to check whether the data agree with certain prediction. These predictions are hypotheses about variables measured in the study. A hypothesis is a statement about some characteristic of a variable or a collection of variables.
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Introduction A significance test is a way of statistically testing a hypothesis by comparing the data to values predicted by the hypothesis. Data that fall far from the predicted values provide evidence against the hypothesis.
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Introduction A significance test provides a way of judging whether a particular value for the parameter is plausible. Remember that the estimation method of confidence intervals provides a range of the most plausible values for a parameter. Both methods are based on the foundations of probability, through the sampling distribution of the estimator of the parameter.
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Topic Outline Elements of significance tests Large sample tests for quantitative and qualitative data Small sample tests for quantitative and qualitative data Decisions and types of errors in tests of hypotheses
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Elements of Significance tests Significance tests have five elements: 1. Assumptions 1. Hypotheses 2. Test statistic 3. P-value 4. Conclusion
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Assumptions Assumptions are often made about the sampling method, type of variable, sample size and form of population distribution. Assumptions Nearly all tests require random sampling . Tests for quantitative variables refers to means , whereas tests for qualitative variables refer to proportions .
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Assumptions Assumptions Large samples tests for proportions (n >10 / [min(π o , 1- π o )]) and for means (n >= 30) require no assumption about the population distribution. The Central Limit Theorem implies approximate normality of the sampling distribution, regardless of the population distribution. Small sample tests for means use the t distribution and small-
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Topic_7.0___Statistical_Inference___Significance_Tests -...

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