POS3713 Understanding Political Science Research Test 3 Study Guide Five Step Model for Hypothesis Testing This is on here to allow you to think about the process 1 Make assumptions and determine if they are met 2 State the null hypothesis 3 Determine the sampling distribution 4 Calculate the test statistic 5 Interpret the results Compare your test statistic to the critical value from the sampling distribution Remember you need to calculate the degrees of freedom to determine the critical value If the test statistic is larger then reject the null Samples vs Population o Population all occurrences of our cases of interest If we care about wars it is ALL wars Data for every possible relevant case o Sample a subset from within that population A subset of cases that is drawn from an underlying population Hopefully chosen randomly Most calculations we do are sample 95 Confidence etc Only do sample when we do not have all population information EX QUEST When you have the population information you need to calculate the error ANS False Statistical Inference population o We have the sample and now we are going to infer something about o We need to know how the sample and the population link o The process of using what we know about a sample to make probabilistic statements about the broader population Simple Random Sample o A sample such that each member of the underlying population has an equal probability of being selected o Every case has an equal probability of being chosen o Problem with internet surveys person must have internet Sampling Distribution o This is where the statistics start to come in o Is distribution of a calculated statistic taken from repeated samples within a population an infinite number of times o The reason we care about this is because it is telling us about the uncertainty of our estimates o A hypothetical distribution of sample means Central Limit Theorem o About the sample distribution of the mean o It says three things The sampling distribution of the mean is normally distributed Bell curve Our mean from any one sample is a good estimate of the mu or true meaning sample mean The standard deviation of the sampling distribution gets smaller as the sample size N gets bigger o Standard Error of the Mean The standard deviation of the sampling distribution of sample means Is our measure estimate of the standard deviation of the sampling distribution The standard error gets smaller as the sample size N gets larger Smaller standard error the more confident we are about what is going on in the population 95 Confidence Interval of the Mean o A probabilistic statement about the likely value of a population characteristic based on the observations in a sample o Assuming a large sample sign it s the mean o Only formula that has two answers o We calculate a sample mean and that s our estimate of the sample mean You take the sample mean 1 96 and multiple it by the standard deviation o At the lowest we think it is the mean minus 1 96 x the standard deviation o At the highest we think it is the mean plus 1 96 x the standard deviation o Confidence interval shrinks as the sample size gets larger o Why 1 96 It s about the critical levels The Different Distributions o Standard Normal Distribution A bell shaped statistical distribution that can be entirely characterized by its mean and standard deviation The sampling distribution of the mean will have a standard normal distribution 68 95 99 Rule o A useful characteristic of the normal distribution which states that moving 1 2 and 3 standard deviations from the mean will leave 68 95 and 99 of the distribution s area under the curve o T Distribution Is essentially the normally distribution except it corrects for cases with small sample sizes EX Remember the beer company example Critical Values o A predetermined standard for a statistical test such that if the calculated value is greater than the critical value then we conclude that there is a relationship between the two variables and if the calculated value is less than the critical value we cannot make such a conclusion All you need to know is the following levels o 1 64 10 level o 1 96 05 level To know which one to use on test it will say we are looking for a 95 value or a 90 value or 05 01 If it doesn t say assume 05 At a large distribution size t distribution and normal distribution are the same The t statistic o 2 Distribution As the sample size gets larger you are more likely to find that there is a relationship between the two variables even though it doesn t say how strong that relationship is Not a measure of association Just telling us they appear to be related Do it when your independent variable is categorical and your dependent variable is also categorical Important thing to remember is to start with the raw numbers not the percentages Calculate the marginal totals Think about the expected table The point is that we want to create a table called the expected table that says if there were no relationship what would that table look like The Research Hypothesis The Null Hypothesis o The relationship we expect to see between two variable o The two variables are not related o Any relationship between the two variables in the sample is a result of random chance If we polled 1000 football fans and asked region they were from and asked whom they think should play in the super bowl People from FL say FSU people from Oregon say Oregon The null hypothesis is that it doesn t make a difference o The probability that we would see the relationship that we are finding because of random chance o Essentially the probability that the null hypothesis is true o Given our data what is the probability that the null hypothesis is true o 05 is a p value o Ranges from 0 1 o The research hypothesis is more likely to be supported with SMALLER p o The null hypothesis is more likely to be supported with larger p values p values values Type I Error o Rejecting the null when the null is true o If we reject the null that means we are saying the evidence supports our research hypothesis but we are making a mistake and our hypothesis is right We want to have a p value smaller than 05 Type II Error o Accepting the null when the null is false o I don t believe there is a relationship but we are wrong Our research hypothesis is true and we do not see that it is Statistical Significance o A conclusion based on the observed data that the relationship between two variables is not due to random chance and
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