inferential Statistics

Hypothesis testing - answer-A statement about the parameters; support or contradict; based on sample evidence (stat) and probability, used to test claims regarding a characteristic (parameter) Population - answer-All subjects or objects possessing some common specified characteristic. Arbitrarily defined by naming its unique properties Parameter - answer-A measurable characteristic do a population (u, sigma...) Sample - answer-Smaller group of subjects or objects selected from a large group (population) Statistic - answer-A measurable characteristic of a sample (x,s,z,t...) Null hypothesis - answer-There is no difference or association between variables that is any greater than expected y chance Alternative hypothesis - answer-The relationship or association or difference that the researcher actually believes to be present; research hypothesis Steps for hypothesis testing - answer-1. Establish hypothesese (null and alt) 2. Significance level- determine what alpha to use to determine statistical significance 3. Stats test- determine what test to use 4. Compare the distribution of the stat to the distribution under the null and report p- value 5. Decision rule: reject or fail to reject null Significance level - answer-Alpha is the probability of making a type 1 error; specified as a small probability range, usually 0.05. P value interpretation - answer-- <1%= overwhelming evidence that supports the alt. hyp. -1-5%= strong evidence to support alt hyp. -5-10%= weak evidence to support alt hyp ->10%= no evidence that supports the alt. hyp Type 1 Error - answer-(alpha): reject null when null is true Type II Error - answer-Beta: we don't reject the null when the null is false Point estimate - answer-When a parameter is being estimated as a single number Interval estimate - answer-When a parameter is being estimated as a range of scores Confidence interval - answer-The level of certainty that the true score falls within a specific range. The smaller the range the less the certainty. 95% CI formula - answer-u=X+-1.96(sigma/sqrt n) 99%CI Fromula - answer-u=X+-2.58(sigma/sqrt n) Test statistic Z - answer-Z= xbar-u/sigma/sqrt n T test - answer-A group of statistics used to determine if a significance difference exists between the means of two sets of data; small n (<30) Sampling distribution - answer-Describes probabilities associated with a statistic when a random sample is drawn from a population Why t test instead of Z test? - answer-Z requires knowledge of the population standard deviation sigma~ usually don't have this information. Use t test for this T test formula - answer-t=Xbar-u/S/sqrt n Where u is the population mean, Xbar is the sample mean and S is the estimator for population standard deviation. One sample t test - answer-Compares the mean score of a sample to a known value~ usually the population mean One sample t test data requirement - answer-Continuous data, small sample, known population mean u One sample t test assumptions - answer-Data is normally distributed, individual observations are independent, sample is randomly drawn Procedure for a t test - answer-1. Null and alt hypo 2. Specify significance level 3. Calculate the t statistic 4. Determine the critical value 5. Compare the t value with the critical value 6. State the conclusion Degrees of freedom - answer-N-1; the number of data points that are free to vary CI for t test - answer-T value will vary depending on degrees of freedom; (1-alpha)100%CI for u=Xbar +-t(s/sqrt n); if the hypothesized value is contained in the CI= insignificant (fail to reject null) Two independent sample t test - answer-- compare population means of two populations -hypotheses are left, right or two tailed -test statistic should be used Two Sample t test assumptions - answer-1. both parent populations are normally distributed 2. random samples were taken from each distribution 3. the population variances of the two populations are equal Procedure for a two sample t test - answer-1. hypotheses 2. significance level 3. compute test statistic 4. determine critical region 5. reject null if test statistic falls in the critical region; fail to reject if it falls outside CR 6. calculate exact p values 7. express results in p values 8. CI 95% or 99% 9. conclusions Two sample t test with unequal variances - answer-adjusted with dF Paired t test - answer-two population means where you have samples in which observations can be paired (i.e pre and post test scores) Paired t test assumptions - answer-1. paired differences are independent 2. paired differences are identically normally distributed (same mean and variance) Procedure for a paired t test - answer-1. calculate the difference between the observations of each pair (di= yi-xi) 2. calculate the mean difference (dbar) 3. calculate the standard deviation of the differences and use this to calculate the standard error of the mean 4. calculate the t statistic 5. use tables for t distribution to compare your value for T to the tn-1 distribution this will give the p value for the test Paired t test test statistic formula - answer-t=dbar-o/sd/sqrt n where d=mean diff between x and y for each case; Sd is the estimate of the standard deviation of the difference df or a paired t test - answer-number of groups - 1; determines critical region One way ANOVA - answer-use when the mean of a variable (dependent variable) differs among three or more groups; drug vs control One way ANOVA data requirement - answer-Dependent variable (DV) has to be continuous and must fulfill assumptions Independent Variable (IV) can have two or more levels (male, female;religion; race) ANOVA Assumptions - answer-1. DV is normally distributed for each of the population 2. the population variances of the DV are the same (homogeneity) 3. the cases represent random samples from the population and the schores on the DV are independent of each other (mutually exclusive) ANOVA violations - answer-non normality; heterogenity of variance among groups; non-indpendence Advantages ANOVA vs t Tests - answer-1. yields accurate and known type 1 error 2. can affect 2 or more independent variable simultaneously 3. more powerful when alpha is held constant 4. robust ANOVA terminology - answer-a) factor: independent variable b) independent measures: seperate sample for each treatment c) level: individual treatment conditions that make up a factor. F ratio - answer-ANOVA: variance between treatments divided by the variance within treatments; or F= treatment effect+ differences due to chance/ differences due to chance F=1 - no treatment effects F>1- some treatment effect (not significant though) Sum of Squares for Total Variation - answer-equal to the sum of the squared deviations of each data point in all the groups from the grand mean Sum of Squares within - answer-total variation that occurs in each group compute each SS deviation of each sub-group seperately and summing the results Sum of Squares between - answer-examines how each group mean varies from the grand mean Gr