Chapter 6 Exam 3 Chapter 6 7 What is the difference between a population and a sample o Population all occurrences of your phenomenon of interest Every person that it happens to or fits the criteria o Sample a subset of the population of interest o This sample is used to infer that the results also apply to the general population If it s a good random sample It should be generalizable Generalization What is statistical inference to the general population o Statistical inference use the stats from the sample to infer that the same occurs or applies Usually do this unless you asked the entire population and then you don t need to infer The conclusion is gathered from every person in that population like everyone taking this class is a popul What are parameters Sample vs population parameters o Parameter traits that can be quantified like averages differences between groups and relationships among variables Sample Parameter sample mean it s an average of the sample X bar Population Parameter Real average of the population Population mean is mu Sample mean estimate of population mean mu with like arrow on top Why use samples rather than observing the population What is simple random sample o Because its more feasible costs less than surveying everyone it s more practical o Simple random sample every case has an equal chance of being selected in the sample Sample parameters from these types of random samples will reflect population parameters Useful because of central limit theorem there is a normal distribution in sample which isn t common in the world bell curve What is the central limit theorem What is it telling us o Central limit theorem says that the sampling distribution will be normally distributed if we were to graph all sample means of many samples sampling distribution If repeated random samples of size N are drawn from any population with mean m and standard deviation s then as N becomes large the sampling distribution of sample means will approach normality with mean and standard deviation o What is it telling us The mean of the sampling distribution will be equal to the true population mean What is a normal distribution o Bell shaped symmetric Mean median and mode are all the same What is nice about the normal distribution o And there is a predictable area under the curve to calculate confidence level from the standard deviations What is the 68 95 99 Rule o 68 of cases fall within one standard deviation of the mean o 95 of cases fall within two standard deviation of the mean o 99 of cases fall within three standard deviations of the mean What is a sampling distribution o If we graphed the sample means for many samples this would show the sampling distribution infinite of samples and their means What happens to our estimates when we increase the sample size or the number of samples taken o As sample size gets larger our sample means are typically closer to the population or true mean more accurate o Larger more like population o Standard error decreases with larger sample What is the standard error of the mean How is it calculated o Standard deviation of the sampling distribution o standard deviation of sample divided by square root of N sample size As we increase our sample size what happens to the standard error of the mean o Standard error decreases with larger sample How do we calculate a confidence interval of a mean What happens to this interval as the sample size increases o Need to know the mean standard deviation and N size Or standard error o 95 confident Sample mean 1 96 standard error or this is the standard o As sample size increases you become more confident Small sample size standard error deviation N is larger less confident Chapter 7 research hypothesis What is a bivariate hypothesis test What is hypothesis testing Do we seek to reject the null or o Bivariate hypothesis testing only two variables are considered at a time Like causal theory X Y Are X and Y related o Hypothesis Testing We need to eliminate the possibility that any difference was just the result of random chance Compare actual relationship between x y in your sample data to what we expect to find if x y unrelated null o Goal is to reject the null hypothesis eliminate chance that any difference observed is a result of random chance not statistically significant What is the Five Step Model for Hypothesis Testing o Make Assumptions and determine if those assumptions were met Usually assume random sampling was done central limit theorem o State the null Typically there is no difference Exception in directional research hypotheses the null might be different o Determine the sampling distribution and critical region Sampling distribution and the test statistic will depend on the particular hypothesis you re testing o Interpret the results Was the null Hyp Rejected Is the relationship statistically significant What determines which type of hypothesis test we use o The level of measurement for our independent and dependent variables What type of test is most appropriate given our independent and dependent variable i e Chi squared vs correlation coefficient vs difference of means test Typically what is the confidence level we seek in our hypotheses o 5 That is if our test statistic has only a 5 chance of occurring if the null is true then we will reject the null hypothesis What is a p value What does it tell us What doesn t it tell us What are the limitations of p values o P value comes from hypothesis testing and is used to evaluate null hypothesis The probability that we will see the relationship we are finding because of random chance Lower p value more confidence Less random chance probability Between 0 1 Larger sample size lower p values more confident o What does it tell us the probability we would see the observed relationship in the sample data if there were truly no relationship in the population random chance Manipulation make sample size bigger to reduce p value by reducing the standard o Doesn t tell us How valid our measures are o Limitations error Not comparative to other p values Not conclusive for causality What is a chi square test What does it tell us What are the steps for calculating a chi square statistic How do we calculate degrees of freedom o Chi squared test or Tabular Analysis two categorical variables Study a cross tabulation to figure out if there are differences between groups So we are going to calculate the table we would have expected to see if there was no
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