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On-line resources http://wise.cgu.edu/powermod/index.asp http://wise.cgu.edu/regression_applet.asp http://wise.cgu.edu/hypomod/appinstruct.asp http://psych.hanover.edu/JavaTest/NeuroAnim/stats/StatDec. html http://psych.hanover.edu/JavaTest/NeuroAnim/stats/StatDec. html http://psych.hanover.edu/JavaTest/NeuroAnim/stats/t.html http://psych.hanover.edu/JavaTest/NeuroAnim/stats/CLT.html Note demo page

Power ->.10.20.30.40.50.60.70.80.90 Effect size |.01215383113144179219271354.0651014192430364457.1535681012141722 If you think that the effect is small (.01), medium, (.06) or large (.15), and you want to find a statistically significant difference defined as p<.05, this table shows you how many participants you need for different levels of “sensitivity” or power. Statistical power is how “sensitive” a study is detecting various associations (magnification metaphor)

Power ->.10.20.30.40.50.60.70.80.90 Effect size |.0170116156194232274323385478.06132026323845536277.156811131518202429 If you think that the effect is small (.01), medium, (.06) or large (.15), and you want to find a statistically significant difference defined as p<.01, this table shows you how many participants you need for different levels of “sensitivity” or power.

What determines power? 1.Number of subjects 2.Effect size 3.Alpha level Power = probability that your experiment will reveal whether your research hypothesis is true Power = 1 - type 2 error Power = 1 - beta

How increase power? 1.Increase region of rejection to p<.10 2.Increase sample size 3.Increase treatment effects 4.Decrease within group variability

Study featurePractical way of raising power Disadvantages Predicted differenceIncrease intensity of experimental procedures May not be practical or distort study’s meaning Standard deviationUse a less diverse population May not be available, decreases generalizability Standard deviationUse standardized, controlled circumstances of testing or more precise measurement Not always practical Sample sizeUse a larger sample sizeNot practical, can be costly Significant levelUse a more lenient level of significance Raises alpha, the probability of type 1 error One tailed vs. two tailed test Use a one-tailed testMay not be appropriate to logic of study

What is adequate power?.50 (most current research).80 (recommended) How do you know how much power you have? Guess work Two ways to use power: 1. Post hoc to establish what you could find 2. Determine how many participants need

Outcome statistically significant Sample SizeConclusion YesSmallImportant results YesLargeMight or might not have practical importance NoSmallInconclusive NoLargeResearch H. probably false

5 steps to hypothesis testing 1.Restate the research question as an alternative hypothesis and a null hypothesis about the populations. 2.Determine the characteristics of the comparison distribution. 3.Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. 4.Determine your sample’s score on the comparison distribution. 5.Decide whether to reject the null hypothesis.

Comparison table

Terms to know Random selection Convenience or haphazard selection Random assignment http://onlinestatbook.com/stat_sim/sampling_dist/index.html

Example 1 A doctor gives a patient a new type of anti- depressant. Is there any improvement compared to a larger population of depressed population? Assume that depression scores follow a "normal curve" (Population) M = 69.5 SD = 14.1 X = 41

5 steps 1. Convert research questions to statistical hypotheses. Null Hypothesis: Alternative Hypothesis 2. What are the characteristics of our comparison distribution? Why can we use the normal curve? Not all distributions are normal. 3. Determine "cut-off" scores. Conventional level of statistical significance One tailed vs. two tailed 4. Determine your observation or sample score. Convert observation to Z score. 5. Accept or reject the NULL hypothesis. How would we write it down?

Z score distribution http://davidmlane.com/hyperstat/z_table.html

Example 2 Is memory affected by stress? Ask 25 people to give a talk and then remember a set of photographs. Mean recall = 48, SD=7, General population mean=53 Shift to a sample of observations from a single observation. 3 key characteristics of a distribution of means. – Mean of distribution of means is the same as the original population of individual scores. – Spread of distribution is narrower than spread of individual scores (so we need to correct for that!) – The shape is normal (but requires a sample size of 30 and normal distribution of scores for the sample to make this assumption)

Distribution of means graphs

How do we correct the problem? Formula

Comparison of three types of distributions

What if don’t know population? Move to t-tests

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