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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 [onenumber]o Sample mean and standard deviation are the point estimates of the population mean and standard deviation- Confidence interval: range of values define by confidence level within which population parameter is estimated to fall- Confidence level: likelihood, % or probability that specified interval will contain population parametero 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 confident, more preciseo 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- Distribution of random sample: use observable info about sample [mean and standard deviation]- Sampling distribution: theoretical normal distribution whose mean and standard deviation are unbiased estimates of population parameters. Allows us to infer parameters from known statistics- Rules: Even if population distribution is skewed, the sampling distribution of the mean is normally distributed o As sample size increases, mean of sampling distribution becomes equal to population mean & standard error of mean decreases- 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 thepoint estimate contains the actual population mean - Margin of error: value added and subtracted from the mean – produces larger and smaller number than meanChapter 10: Relationships between two variable [cross-tabulation]- Bivariate analysis: statistical method designed to detect and describe relationship between 2 variables- Cross-tabulation: technique for analyzing relationship b/w 2 variables that have been organized in a table- 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 Independent variable’s categories in rows, divide each cell by row totals- Strength of relationship: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]- Variable is ‘controlled for’ when we take into account its effect on variables in bivariate 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 intervene b/w IV & DVo Elaboration specifies different conditions under which the original bivariate relationship might hold- 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’by introducing control variableo Ideally, there is a direct causal relationship: a bivariate relationship that can’t be accounted for by other variableso In this case control variable becomes known as extraneous variable- How to test relationship for spuriousnesso Partial table: bivariate table that displays relationship between IV and DV while controlling third variableo Divide observations into subgroups on basis of control variable [# subgroups = # categories of control variable]o Re-examine relationship between original 2 variables separately for control variable subgroupso Compare with original bivariate relationship for total group - Intervening variable: control variable that follows independent variable but precedes dependent variable in causal sequenceo Independent variable affects control variable and control variable affects dependent variableo Ex: religion (IV) preferred family size (intervening control variable) support for abortion (DV)- Conditional relationship: control variable’s effect on dependent variable is conditional on interaction with IVo Relationship between IV and DV will change according to different conditions/categories of control variableChapter 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 are identical- Chi-square test: inferential statistics technique designed to test for significant relationship between 2 variableso Only used with nominal or ordinal variableso Want to see if relationship in sample is real and if it exists in the population, not just the sampleo Significant relationship if chi-square test tells us there’s a real relationship in population, not just sample- 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 supports]- 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 results are significant o Expected frequencies: cell frequencies that would be expected in bivariate table if 2 tables were

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