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What are three factors affecting experiments? 1) Chance/random factors beyond control 2) Random variation in each sample 3) Different sample sizes What do inferential statistics allow you to do? Inferential statistics allow you to solve problems of extraneous factors. They allow you to perform significance testing and allow you to ask if it is a chance result (will you come to the same conclusion if you repeat the experiment; is it just chance variation in the data; is the null hypothesis really true) What two things do you need to know in order to do inferential statistics? 1) If the null hypothesis is true, what is the probability of getting the result (or a greater one) by chance? 2) Is this probability small enough to ignore? What do inferential statistics compute? A p-value. What is a p-value? p-value: the probability of getting the result (or a greater one) you obtained in your study by chance, assuming the null hypothesis is true. What do you compare a p-value against? The alpha value. What is a type 1 error? Type 1 error: you conclude there's a difference in your study, but they are actually the same. 'Miss' What is a type 2 error? Type 2 error: you conclude there is no difference in the study, but they actually are different. 'False alarm' What is the relationship between type 1 errors and type 2 errors? Decreasing type 1 errors raises type 2 errors and vice versa. What is the alpha level? The alpha level (AKA significance level because it determines what 'statistically significant' results are) is the probability that a statistical test will generate a false-positive error (type 1 error). What is the significance level also known as? The alpha level. What is the alpha level in psychology and why? <5% that a reported finding is due to chance. It is a good balance between type 1 errors and type 2 errors. If you have p= .050 or smaller, what do you conclude? You have found a 'real' difference and the findings are statistically significant. If you have a p greater than .050, what do you conclude? There is no difference and the findings are not statistically significant. What does the alpha level not inform you of? It does not inform you directly of the chance of making a type 2 error. What is the null hypothesis? Null hypothesis = definition of chance; no significant difference. If the p-value is greater than .050, we must accept the null hypothesis. What is a 1-tailed test? What is the p-value? Directional hypothesis. p=.050 in the direction stated. What is a 2-tailed test? What is the p-value and why? Non-directional hypothesis. Effect present but no direction stated. p=0.025 in both directions as using 0.050 in both directions would increase alpha-level to 0.100 and increase chances of making a type 1 error. Which test is more significant: 1-tailed or 2-tailed? Why? 2-tailed test is always more significant, as some values that would be significant with a 1-tailed test would not be with a 2-tailed test. Which test should you always use according to the University of York unless an effect CANNOT go in the other direction (e.g. relationship between age and height in children)? 2-tailed test. What is a point estimate? Point estimate: using a single number as your estimate of an unknown quantity. What is an interval estimate? Interval estimate: using a range of values as your estimate of an unknown quantity. What is a confidence interval? Confidence interval: when an interval estimate is accompanied by a specific level of confidence (or probability). What does a confidence interval show us? A confidence interval shows us the probability of the population mean falling within a certain range of values. What confidence intervals do we use in psychology and why? 95% confidence intervals, as we are mostly interested in p=.050. How do you calculate a lower confidence limit and an upper confidence limit? Lower confidence limit: Mean - (t * SEM) Upper confidence limit: Mean + (t * SEM) <b> t = 1.96 </b> For the confidence limit equation, what does t depend on? What is 't' usually? t depends on the degrees of freedom and the level of confidence. In reality, t = 1.96. You can assume this is true. How do you report a confidence interval? E.g. A 95% confidence interval for the mean Beck Depression Index of individuals with schizophrenia is 5.31-16.13. OR Individuals with schizophrenia have a mean Beck Depression Index of 5.31-16.13 (95% confidence interval). What is the relationship between confidence intervals, N, and SEM? Why? The bigger the N, the smaller the confidence interval, and the more precise the estimate. This is because: 1) SEM depends on N (s.d./sqrt(N)) 2) Confidence intervals depend on SEM (mean +/- 1.96 * SEM).