Chapters 5 and 6 Notes (Review)
Chapters 5 and 6 Notes (Review) PSYCH-UA 10 - 001
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PSYCH-UA 10 - 001
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Date Created: 03/06/16
Statistics for the Behavioral Sciences Chapter 5 and 6 Review: Hypothesis testing: The Null Hypothesis Distribution (Ho) is the sampling distribution of the mean. Probability: Alpha: the amount of error we’re willing to make. It is a specific pvalue that we compare to the actual pvalue that we find on the chart. We’re willing to accept this risk of chance 1/20 times, so alpha is .05. Region of Rejection: The area of the normal distribution in which we reject the null hypothesis. These are the smaller areas outside alpha. The probability of getting a result in those areas is so small that it’s probably not due to chance – there’s significance. The Null Hypothesis (H0) When we assume that the population mean (mu) is equal to the sample mean (mu0). This is the given; this is the hypothesis that the researcher often hopes to disprove. The Alternative/Research Hypothesis (Ha) The population mean (mu) is different from our sample mean (mu0). This is the hypothesis we’re usually interested in – the one we hope yields significant/reliable results because it discovers a new finding. Ultimate question: If there is a difference, is there really a reliable/significant difference or is it due to pure chance? We answer this question by looking at where the mean falls in the null hypothesis distribution : The Steps: Hypothetical example: If the mean of a population test score is 50 (with a standard deviation of 5), what are the odds that our class mean will be different? 1. Find the Null Hypothesis (mu0 = mu = 50). The mean egomaniac score for our class is the same as the mean egomaniac score for the general population. 2. Find the Alternative Hypothesis (Ha : mu0 ≠ mu OR mu ≠ 50). The mean egomaniac score for our class is NOT the same as the mean egomaniac score for the rest of the population. * 2tailed experiments are set on a particular theory/direction. Researchers are aware that the results could go both ways. Statistics for the Behavioral Sciences 3. Determine type of statistical test based on sample size (z test if N > 40 and t test if N < 40) –[ though in real life scenarios, work with 100, not 40 ]. 4. Use a statistical test to find either the z or t calculated values. 5. Take your degrees of freedom (n1) to find the corresponding z or t CRITICAL value on the chart. If your degrees of freedom are too high, then (for the purpose of this class), jump to the nearest lower df. 6. Plot your alpha (usually .05) a drawing. If a twotailed experiment, divide alpha by 2 (.05 / 2 = .025) and list .025 values on either side. 7. Plot your calculated and critical values on the same drawing. Compare the calculated value (what you found using the formulas) to the critical value (what you found on the chart). If zcalc > z crit and p < .05, then we REJECT the null. Scores are significant. If zcalc < zcrit and p > .05, then we FAIL TO REJECT the null. Scores are not significant. (The above goes for tscores as well ^). ***Reminders: p is probability, so p < .05 when zcalc falls outside alpha (or in the smaller region). But p > .05 when zcalc falls in between the two alphas (the bell curve region). 8. The Confidence Interval – how confident you are that the population mean falls within your two interval values. Use the null to test for significance. If null falls within the interval, you fail to reject. If null falls outside the interval, you reject. X z s critX Formula (the same goes when working with tcritical values): Determining Errors: Type 1 Error: Rejecting the null hypothesis when it shouldn’t have been rejected. (Saying there’s significant results when it was due to chance all along) Type 2 Error: Failure to reject the null hypothesis, when it should have been rejected. Saying there’s no result when there actually was a significant result all along). In real life scenarios, Type 2 errors are more dangerous to make because it’s worse to say “Oh, there’s no significance here” when there really was something significant. What we were SUPPOSED to do (reality) What we chose to do (below ) Fail to Reject Reject the Null Fail to Reject Null Correct Conclusion Type 2 Error Reject Null Type 1 Error Correct Conclusion Statistics for the Behavioral Sciences Power: (1Beta) the probability that we correctly rejected the null hypothesis, and correctly found significant results.
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