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Tests of Significance for Proportions:

Tests of Significance for Proportions:. Formalizing what you have been doing all along. Recall the Kissing Couples study (from 04/04). Researchers observed 124 randomly selected couples from various age groups kissing in public places in the U.S., Germany, and Turkey.

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Tests of Significance for Proportions:

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  1. Tests of Significance for Proportions: Formalizing what you have been doing all along

  2. Recall the Kissing Couples study (from 04/04) Researchers observed 124 randomly selected couples from various age groups kissing in public places in the U.S., Germany, and Turkey. 80 couples were observed to lean their heads to the right when kissing, for a sample proportion of p-hat = 0.645 The logic of what we did: We made various assumptions about the true population proportion: π = 0.5, π = 2/3, π =3/4 We tested the plausibility of each assumption by finding the likelihood of obtaining the observed sample proportion under that assumption An assumed population proportion was judged to be implausible IF the observed sample proportion had low probability of occurring (and was thus very surprising) under that assumption. We used the CLT.

  3. We informally introduced the key idea of statistical significance: A sample result is said to be statistically significant if it is unlikely to occur (i.e., has low probability) due to random sampling variability alone. Today we will formalize that logic (line of reasoning) by specifying it as a multi-step procedure and casting it in terms of formal symbols. The reasoning is the same as before. The only new aspect here is its proceduralization and the use of formal symbols to express that reasoning as a formal test of significance (for proportions)

  4. Activity 1: Revisiting Kissing Couples 1

  5. Activity 1: Watch Outs !! The p-value is NOT the probability that the null hypothesis is true. Rather, it is the probability of obtaining a sample result at least as extreme as the one observed when the null hypothesis is (assumed) true. Always state your conclusion in terms of the context. Statements like “reject H0 and conclude that π > .5” are incomplete. You must express such conclusions in context by saying, “The sample data provide very strong evidence that more than half of all kissing couples lean to the right”. Always include ALL six steps of a significance test: 1. Identify and define the parameter 2. State the null and alternative hypothesis, preferably in words as well as symbols 3. Check the technical conditions 4. Calculate the test statistic 5. Report the p-value 6. Summarize your conclusion in context, using a test decision if a significance level is provided

  6. Activity 2: Revisiting Kissing Couples 2 Watch Out!! Be careful never to accept a null hypothesis! The logic of significance testing is based on assessing whether there is enough statistical evidence against the null hypothesis, NEVER evidence in favor of it.

  7. Summary of the significance test procedure

  8. Summary of the significance test procedure 6. Summarize your conclusion in context, using a test decision if a significance level is provided

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