POS 3713 Exam 3 Study Guide 1 What is the difference between a sample and population and why and to what extent do we care about each Sample subset of cases we use to collect data Population all of the occurrences in your phenomenon of Why we care about each we need samples to learn about interest populations 2 What is a normal distribution and what information can we learn from its mean and standard deviation Normal Distribution the symmetrical bell shape curve that allows us to estimate the percent of cases that fall within the distance of the mean mean median mode Standard deviation thus comes the 68 95 99 rule o 68 of cases fall within one standard deviation form o 95 of cases fall within two standard deviations from o 99 of chances fall within three standard deviations the mean the mean form the mean Mean true population parameter and on average that is 95 of then time 3 What is the Central Limit Theorem How does it allow us to calculate the uncertainty of our estimates of the population Central Limit Theorem even if a distribution is not normally shaped if we can take an infinite number of samples the mean of those samples would be normally distributed We can estimate the population parameter using sample statistic 4 What is random sample and how does it differ from random convenience Why does the Central Limit Theorem only apply to random sample Random Sample when each member of the population has an equal chance at being randomly selected Convenience Sample a non random selection of sample Why only random sample non random selection does not help us build bridges between sample and population our outcome would not be accurate 5 How do you interpret a 95 confidence interval When the population mean lies within two standard errors of the mean Example question and answer he gave me if George s Bush approval rate in the US is between 33 and 36 how can we interpret the confidence interval We are 95 confident that Bush s approval rate is between 33 36 6 How does sample size affect the standard error of the mean Larger sample sizes reduce the size of standard error smaller sizes increase the size of standard error o It s easier to make inferences about the population with a larger sample size 7 What is the P value What does it tell us not tell us P Value probability value ranging between 0 to 1 that is the probability that we would see the observed relationship between 2 variables in our sample if there were no relationship in the population Tell us the probability we are finding is due to random selection Does not tell us whether the observed relationship is causal and the strength of association between X Y 8 What is the Null Hypothesis and how does it relate to the P Value What is an alternative hypothesis incorrect Null Hypothesis what we expect to observe if our theory is Relation to P Value if there is a covariation between X Y the null states there is no covariation Alternative hypothesis what we expect to see if our observed theory is correct 9 What is the difference between one and two tailed tests How do we choose the appropriate one One Tailed a parameter is either positive or negative and not just different from zero Two Tailed used if we do not know the direction Choosing the appropriate one we choose the one most consistent with our theory 10 What is statistical significance What does it mean if a relationship is not statistically significant Statistical Significance when the relation being observed between two variables is less than 05 it is due to chance alone Not significant prevents from rejecting the null hypothesis 11 What are bivariate hypothesis tests and how do we determine which is most appropriate to test any given hypothesis Bivariate hypothesis only two variables considered at a time to help us answer is X is related to Y How do we determine when the dependent variable and the independent variable is categorical we use a difference of means test o The 3 Bivariate tests Categorical IV Categorical DV Tabular Categorical IV Continuous DV Difference of Continuous IV Continuous DV Correlation Analysis means Coefficient 12 What is the difference between nominal ordinal interval and ratio variables Nominal different values represent difference in kind not quantity Ordinal different values represent difference in rank between units Interval represent exact amount of characteristics being measures Ratio similar to interval except the value of 0 is meaningful 13 How and to what extent do these tests help us overcome the four hurdles of establishing causalities Answers if X is related to why but does not answer any other questions which is hurdle 3 only answers hurdle 3 14 How do you interpret a Correlation Coefficient Correlation Coefficient measure of strength of association between continuous IV and continuous DV o If all points line up and are positive correlation coefficient is equal to 1 if all points line up and are negative the correlation coefficient is equal to 1 o Otherwise it lies between positive and negative 1 All we care about is the consistency and direction of these 15 How do you assess a relationship in a Tabular Analysis Cross Tabs Should be able to just by looking at the chi squared statistics and determine the difference between data in the table assess what relationship is in the sample 16 What does difference of means tell us If categorical IV and continuous DV are statistically significant 17 Know how to calculate and interpret Standard error of the mean standard deviation of the sampling distribution of a statistic Margin of error statistic expressing the amount of random sampling error in a survey s results 95 confidence interval of the mean reflects a significance level of 0 05 A chi squared test of a tabular analysis sampling distribution of the test statistic is a chi squared distribution when the null hypothesis is true Difference of means test and its associated t test significance of differences between a sample mean and a perhaps hypothetical true mean Can be assessed using a t test
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