Test 3 Study Guide Five Step Model for Hypothesis Testing 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 than the critical value you can reject the Null Hypothesis Samples vs Population Use sample parameters or statistics to estimate what is occurring within a population Statistical Inference the process of drawing conclusions from data that are subject to random variation for example observational errors or sampling variation Simple Random Sample each member of the population is equally likely to be chosen at any time in the sampling process Sampling Distribution Each sample we take is one of many samples that we could have chosen It infers the idea that if we took an infinite number of samples and graphed them the Sampling Distribution would show you the plot or layout of the results A normally distributed sample would be a bell curve Central Limit Theorem For means With a large sample size the standard deviation will be normally distributed The sampling distribution of sampling means will approach normality the standard deviation The standard error of the mean will the standard error of the sampling distribution 95 Confidence Level of the Mean X Bar 1 96 Standard Dev of the Sample Sample Standard Normal Distribution the mean median and mode are to zero the standard deviation is one and there is a 95 confidence interval 68 of the sample will fall within 1 Standard Deviation from the mean 95 of the sample will fall within 2 Standard Deviations from the mean 99 of the sample will fall within 3 Standard Deviations from the mean T Distribution For a large sample size t 1 96 p values 0 05 t 1 64 0 10 The student s t distribution steps 1 Calculate the test statistic 2 Determine the degrees of freedom 3 Compare the test statistic to the critical value On test if no sample size is given assume it is x Distribution Easiest Hypothesis test to preform it is a test of statistical independence Uses tabular analysis categorical data Steps 1 Calculate the margins of your table 2 Calculate the Expected Table the row value multiplied by the column value 3 Observed Data Expected Data Expected Data 4 Add values to get x 5 Calculate the degrees of freedom to find the critical value 6 x needs to be larger than the critical values The Research Hypothesis the relationship that we expect to see between groups in our research The Null Hypothesis the statement that there is no relationship between variables Hypothesis Testing comparing x and y relationship in a sample to what we would observe if x and y were unrelated P values the probability that there is no relationship among variables P values range from 0 1 The closer to 0 the more confident you are in your results You want at least a 95 confidence rate in you stusy which would require the p value to be 0 05 The smaller the p value the less chance you will have a Type 1 error The smaller the p value the higher chance you will have a Type 2 error Key Point P values are not conclusive to causality they are susceptible to manipulation Type 1 Error Rejecting the Null Hypothesis when the Null is true Type 2 Error Accepting the Null Hypothesis when the Null is false Statistical Significance very confident that two variables are associated Given our sample we can rule out the possibility of random chance Substantive Significance measure of significance between two variables this is used more for arguments as to why statistics actually matter Measure of Association determines the strength of a relationship between variables Cautionary Note Test of Significance is NOT Measure of Association Tabular Analysis with x Degrees of Freedom Calculated by of rows 1 of columns 1 If x 0 there is no relationship and you accept the Null Hypothesis The Correlation Coefficient r correlation as a measure of covariation r the measure of association between two continuous variables It is a linear relationship ranging from 1 to 1 If r 0 there is no relationship again accept the Null The closer to either extreme 1 or 1 the more confident you can be With a large r or very large sample you can more confidently reject the Null If r 1 there is a perfect positive correlation f r 1 there is a perfect negative correlation This would mean we could exactly predict the dependent value Covariation the extent to which two variables move together and measures the amount of correlation Positive Covariance As X increases or decrease Y tends to increase or decrease Negative Covariance As X increases or decreases Y tends to decrease or increase
View Full Document
Unlocking...