POS3713 Study Guide Exam3 1 5 Step Model for Hypothesis Testing a Make assumptions and determine if they are met b State the null hypothesis c Determine the sampling distribution d Calculate the test statistic e Interpret the results i Compare your test statistic to the critical value from the sampling distribution 1 Remember you need to calculate the degrees of freedom to determine the critical value 2 If the test statistic is larger then reject the null 2 Samples v Population a Samples i A subset of a population b Population i Set of objects people that conform to the unit of analysis object being studied ii Data for every possible relevant case The population is the set of objects or entities that conform to the unit of analysis It is a rare occurrence that social scientists will make use of data pertaining to the entire population Different than sample 3 Statistical Inference 4 Simple Random Sample a Using what we know is true about one sample to infer what is likely about a population a A sample in which researchers draw a sample of data on the basis on randomness meaning that each member of the population has an equal probability of being selected in the sample If a random sample is large enough one can draw confident inferences about the population by observing the sample 5 Sampling Distribution 6 Central Limit Theory a The unofficial sovereign of probability theory a Selecting a subset of cases from a population so it can be observed to draw inferences b Given a large sample size the mean of all samples from a population will be equal to the mean of the population as a whole c Standard Normal Distribution i bell curve ii symmetrical about its mean iii mean median and mode are equal iv has a predictable area under the curve v 68 95 99 Rule 1 68 of cases fall in one standard of the mean 2 95 of cases fall in two standard deviations of the mean 3 99 of cases fall in three standard deviations of the mean d T Distribution ii Critical Values i The sampling distribution for the correlation coefficient 1 Value for the sample statistic that yields the significance level e X Distribution chi squared i Test for tabular association formula v shows whether or not the differences in a Theory used to develop hypothesis about the relationship between x and y and whether theory are statistically significant 7 The Research Hypothesis they are negatively or positively related 8 The Null Hypothesis a Where there is no relationship between x and y i Prediction made if theory were wrong 9 P Values a The probability that we would see the relationship that we are finding because of random chance The lower the p value the greater the confidence we have that there is a systematic relationship between the two variables for which we estimated the particular p value 10 Type I Error 11 Type II Error a Rejecting the null when the null is true a Accepting the null when the null is false 12 Statistical Significance a If the p value is less than the significance level or equivalently if the value of the statistic in your sample is in the critical region it is reasonable to reject the null hypothesis and conclude that the hypothesis is likely correct The relationship measured between X and Y as a consequence is deemed statistically significant 13 Substantive Significance a Measures of Association 14 Tabular Analysis with the X test a Used when variables can be categorical or ordinal b Dependent Variable is in rows and Independent Variable is in columns c Degrees of Freedom i r 1 c 1 as sample size increases we become more confident about our ability to a The measure of the extent to which the relationship between two variables approximates predict things about the population 15 The Correlation Coefficient r a linear relationship b T test for statistical significance of r 16 Difference of Means Test a Hypothesis test in which one compares observed results with what we would expect if there were no relationship between x and y i Develop hypothesis about relationship between means of x and means of y ii Establish a null hypothesis iii Draw random sample iv Establish operational definitions and measure x and y v Measure relationship between x s and y s vi Determine p value vii Decide whether to reject null hypothesis
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