# VCU STAT 210 - 232247731-Statistic-Cheat-Sheet (2 pages)

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## 232247731-Statistic-Cheat-Sheet

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- School:
- Virginia Commonwealth University
- Course:
- Stat 210 - Basic Practice of Statistics

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Sample proportion The mean value of is denoted by and the standard deviation of is denoted by Rule 1 This means that the values from many different random samples will tend to cluster around the actual value of the population proportion Rule 2 Rule 3 when n is large and is not too near 0 or 1 the sampling distribution is approximately normal The Central Limit Theorem can safely be applied if n 30 Central Limit Theorem is well approximated by a normal curve even when the population distribution is not normal confidence interval estimate specifies a range of plausible values for a population characteristic confidence level associated with a confidence interval is the success rate of the method used to construct the interval A statistic that is unbiased and has a small standard error is likely to result in an estimate that is close to the actual value of the population characteristic Margin of error a statistic is the maximum likely estimation error It is unusual for an estimate to differ from the actual value of the population characteristic by more than the margin of error Margin of error M solving for n If the sample size is smaller than 10 of population size M is adjusted by finite population correction factor Since this correction factor is always less than 1 the adjusted margin of error will be smaller confidence interval for a population proportion margin of error Interpretation of Confidence Interval You can be 95 confident that the actual value of the population proportion is included in the computed interval Interpretation of 95 Confidence Level A method has been used to produce the confidence interval that is successful in capturing the actual population proportion approximately 95 of the time An alternative to the large sample z interval mod hypotheses are always statements about population characteristics and never about sample statistics Never state a null or alternative hypothesis using sample statistics A hypothesis test uses sample data to choose between two competing hypotheses about a population characteristic If the null hypothesis is not rejected the conclusion is fail to reject y B y y want to imply that you have evidence that the null hypothesis is true P value specifies how likely it is that a sample would be as or more extreme than the one observed if H0 were true Test statistic Knowing the value of the test statistic allows calculation of the corresponding P value Categorical or numerical Number of sample or treatment Question type Study type Estimation Sample Hypothesis Sample Estimation Sample Hypothesis Sample Estimation Sample Numerical variable 1 Hypothesis Sample Numerical variable 1 Estimation Sample Numerical variable 2 Hypothesis Sample Numerical variable Categorical variable Categorical variable Categorical variable Categorical variable Hypothesis Sample Numerical variable Estimation Sample Numerical variable One Sample z Confidence Interval for a Proportion 1 One Sample z Test for a Proportion 1 2 test statistic Method Two Sample z Confidence Interval for a difference in Proportion Two Sample z Test for a difference Proportion 2 One Sample t Confidence Interval for a mean One Sample t Test for a mean Two Sample z Confidence Interval for a difference in mean Two Sample z Test for a difference mean 2 More than 2 More than 2 H0 is true Type I X Reject H0 Fail to reject H0 H0 is False Power 1 Type II Power and n Power and Power and The power of a test is the probability of rejecting the null hypothesis ANOVA F test Multiple comparisons Upper tailed test Ha p hypothesized value Lower tailed test Ha p hypothesized value Two tailed test Ha p hypothesized value If z is positive P value 2 area to the right of z If z is negative P value 2 area to the left of z At least More than x 1 P X x Less than X x 1 P X x Difference between two population proportions Rule1 Rule 2 Confidence interval for the difference in population proportions is Test statistic z crit IF the H0 P1 P2 0 is true a combined estimate of the common population proportion is Result of a hypothesis test can never show strong support for the null hypothesis In twodifference between two population proportions based on the outcome of a hypothesis test Difference between two population means Rule1 1 2 y convinced that there is no Rule 2 Test statistic df V1 V2 If the population variances are equal the pooled t test has a slightly better chance of detecting departures from the null hypothesis than does the two sample test of this section d t Random assignment to treatments is critical ANOVA SSgroup df a 1 SStotal df N 1 SStotal SSmodel SSerror MSgroup MSerror p value P F a 1 N a Fobs Fobs Fcrit reject H0 Model 1 Grand mean model xij j Model 2 Group mean model Xij j Two way ANOVA SStotal df n 1 SSmodel df 1 df n 2 SSerror SStotal SSmodel SSerror MSmodel MSerror p value P F 1 n 2 Fobs Fobs Fcrit reject H0 Model 1 yi Overall mean Model 2 yi Slope model Model 3 yij j treatment Model 4 yij j j Treatment slope Model 5 yij j j interaction Correlation Coefficient Strength 1 strong 0 8 moderate 0 5 weak 0 5 moderate 0 8 strong 1 Least Squares Regression Line Line that minimizes the sum of squared deviations Residual Difference between an observed y value and the corresponding predicted y value Coefficient of Determination Proportion of variability in y that can be attributed by the relationship of x and y Standard Deviation of Least Squares Regression Line Typical amount by which an observation deviates from the least squares regression line r Sum of Squared Deviations b r2 1 se a SSRESID SSTO SSE SSreg

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