Chapter 8 Estimation Estimation a process whereby we select a random sample from a population and use a sample statistic to estimate a population parameter Inferential statistics generalize what we know about a sample to find out about population Point estimate sample statistic used to estimate the exact value of a population parameter one number standard deviation parameter is estimated to fall parameter confident more precise o Sample mean and standard deviation are the point estimates of the population mean and Confidence interval range of values define by confidence level within which population Confidence level likelihood or probability that specified interval will contain population o 95 there is a 95 probability that a specified interval doe contain the population parameter 5 chances out of 100 that interval does not contain population parameter Z 1 96 less o 99 we can be 99 percent confident that the true population average income for lower class household is between and Z 2 58 more confident less precise Population distribution end goal is to find out about central tendency and variation in larger group deviation statistics Distribution of random sample use observable info about sample mean and standard Sampling distribution theoretical normal distribution whose mean and standard deviation are unbiased estimates of population parameters Allows us to infer parameters from known Rules Even if population distribution is skewed the sampling distribution of the mean is normally distributed standard error of mean decreases o As sample size increases mean of sampling distribution becomes equal to population mean Researchers do no typically conduct repeated samples of same population use knowledge of theoretical sampling distributions to construct confidence intervals around estimates The standard error of the mean makes it possible to state probability that an interval around the point estimate contains the actual population mean Margin of error value added and subtracted from the mean produces larger and smaller number than mean variables organized in a table Chapter 10 Relationships between two variable cross tabulation Bivariate analysis statistical method designed to detect and describe relationship between 2 Cross tabulation technique for analyzing relationship b w 2 variables that have been Table of two variables is called a cross tab or two way table Method is best for nominal and ordinal level variables Bivariate table displays distribution of one variable across categories of another variable Cell intersection of a row and a column Marginal row totals and column totals in a table Rule for percentaging tables o If you want to see if independent variable affects dependent variable When independent variable s categories are in the columns divide each cell by corresponding column s total Strength of relationship Independent variable s categories in rows divide each cell by row totals o Weak no relationship 0 10 points Moderate 10 25 points Strong 25 points Direction of relationship Positive variables vary in same direction one increases other increases Negative opposite directions Control variable additional variable that gets considered in bivariate relationship third Variable is controlled for when we take into account its effect on variables in bivariate variable relationship Adding control variable elaboration further explore bivariate relationship o Want to make sure it is the IV that affects the DV testing for spuriousness o Also allows us to clarify causal sequence of bivariate relationship introducing variable to o Elaboration specifies different conditions under which the original bivariate relationship intervene b w IV DV might hold by introducing control variable for by other variables Spurious relationship both the IV and the DV are influenced by a casually prior control variable and there is no real relationship between IV and DV Relationship is explained away o Ideally there is a direct causal relationship a bivariate relationship that can t be accounted o In this case control variable becomes known as extraneous variable How to test relationship for spuriousness o Partial table bivariate table that displays relationship between IV and DV while controlling o Divide observations into subgroups on basis of control variable subgroups categories o Re examine relationship between original 2 variables separately for control variable o Compare with original bivariate relationship for total group Intervening variable control variable that follows independent variable but precedes dependent variable in causal sequence o Independent variable affects control variable and control variable affects dependent variable o Ex religion IV preferred family size intervening control variable support for Conditional relationship control variable s effect on dependent variable is conditional on third variable of control variable subgroups abortion DV interaction with IV control variable o Relationship between IV and DV will change according to different conditions categories of are identical between 2 variables sample just sample supports Chapter 11 Chi Square Test Statistical independence absence of association between two cross tabulated variables Percentage distributions of dependent variable within each category of independent variable Chi square test inferential statistics technique designed to test for significant relationship o Only used with nominal or ordinal variables o Want to see if relationship in sample is real and if it exists in the population not just the o Significant relationship if chi square test tells us there s a real relationship in population not Null hypothesis states that there is no relationship b w variables in population statistically independent data disproves Alternative research hypothesis there s a relationship b w variables in population data Alpha level of probability at which null hypothesis is rejected Steps of hypothesis testing o State research and null hypothesis select alpha level specify test statistics being used and calculate compare test statistic to critical value determine by alpha level and determine if o Expected frequencies cell frequencies that would be expected in bivariate table if 2 tables results are significant were statistically independent o Observed frequencies cell frequencies actually observed in bivariate table of sample data o Chi square is a test statistic that summarizes difference b w observed frequencies and o