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This Concept Map, created with IHMC CmapTools, has information related to: STA 215 Flowchart final.cmap, One-Quantitative Variable Two-Independent Populations Chapter 8 1. Are sigma1 & sigma2 known? 2. Are n1 & n2 both ≥ 30? 3. If n1 & n2 are both ណ, are both orginal populations normal? <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> t = ((xbar1-xbar2)-(μ1-μ2))/ </mtext> <msqrt> <mrow> <mtext> ( </mtext> <mmultiscripts> <mtext> s1 </mtext> <none/> <mtext> 2 </mtext> </mmultiscripts> <mtext> /n1)+( </mtext> <mmultiscripts> <mtext> s2 </mtext> <none/> <mtext> 2 </mtext> </mmultiscripts> <mtext> /n2) </mtext> </mrow> </msqrt> </mrow> </math>, What are you measuring on each individual? Categorical Variable(s) One-Categorical Variable Chapter 3, One-Quantitative Variable Two-Independent Populations Chapter 8 1. Are sigma1 & sigma2 known? 2. Are n1 & n2 both ≥ 30? 3. If n1 & n2 are both ណ, are both orginal populations normal? p-value = tcdf(lower,upper,df) df = minimum(n1-1, n2-1), T-test: t = (xbar-mu)/(s/sqrt(n)) p-value = tcdf(lower, upper, df) (when OTS is positive, it is the lower & when OTS is negative, it is the upper) df = n-1 Confidence Interval: xbar +- t*(s/sqrt(n)) s = (((x1-xbar)^2)) +((x2-xbar)^2+....+(xi-xbar)^2)/(n-1) More Chapter 4 Information When to use each inequality key words to look for: ≠ : different, not equal < : less than, smaller, fewer > : greater than, more, larger, p-value = tcdf(lower,upper,df) df = minimum(n1-1, n2-1) More Chapter 8 Information When to use each inequality key words to look for: ≠ : different, not equal < : less than, smaller, fewer > : greater than, more, larger, p comes from null hypothesis p-value = normalcdf(lower,upper,0,1) More Chapter 3 Information When to use each inequality key words to look for: ≠ : different, not equal < : less than, smaller, fewer > : greater than, more, larger, What are you measuring on each individual? Quantitative Variable(s) Two-Quantitative Variables What do you want to know?, What are you measuring on each individual? Quantitative Variable(s) One-Quantitative Variable Two-Independent Populations Chapter 8, One-Quantitative Variable Chapter 4 1. Is sigma known? 2. Is n >= 30? 3. If nណ, is the orginal population normal? T-test: t = (xbar-mu)/(s/sqrt(n)) p-value = tcdf(lower, upper, df) (when OTS is positive, it is the lower & when OTS is negative, it is the upper) df = n-1 Confidence Interval: xbar +- t*(s/sqrt(n)) s = (((x1-xbar)^2)) +((x2-xbar)^2+....+(xi-xbar)^2)/(n-1), Two-Categorical Variables Chapter 5 1. All expected counts ≥ 1 2. At least 80% of expected counts must be at least 5 <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> Expected counts = (row total)(column total)/(grand total)
chi-square = sum((observed-expected)^2/expected)
p-value = chisqrcdf(lower, upper, df)
df = (# rows - 1)(# columns - 1) </mtext> </mrow> </math>, Two-Quantitative Variables What do you want to know? Are they related? Regression Chapter 6, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> Expected counts = (row total)(column total)/(grand total)
chi-square = sum((observed-expected)^2/expected)
p-value = chisqrcdf(lower, upper, df)
df = (# rows - 1)(# columns - 1) </mtext> </mrow> </math> More Chapter 5 Information Hypotheses always stated the same: Null hypothesis: 2 variables are not related (var1, var2) Alternative Hypothesis: 2 variables are related (var1, var2), One-Categorical Variable Chapter 3 Confidence Interval nphat ≥ 10 AND n(1-phat) ≥ 10? <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> phat ± z∗ </mtext> <msqrt> <mtext> phat(1-phat)/n </mtext> </msqrt> </mrow> </math>, What are you measuring on each individual? Quantitative Variable(s) One-Quantitative Variable Chapter 4, One-Categorical Variable Chapter 3 Hypothesis Test np ≥ 10 AND n(1-p) ≥ 10? <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> Z = (phat-p)/ </mtext> <msqrt> <mtext> p(1-p)/n </mtext> </msqrt> </mrow> </math>, Paired Data Chapter 7 Create a difference variable Use Chapter 4 toolbox, 1. Are the residuals normal? 2. Is there constant variability? least squares line formula: y-hat = b + mx Get OTS (t) and p-value from calculator or SPSS More Chapter 6 Information When to use each inequality key words to look for: ≠ : linear relationship < : negative linear relationship > : positive linear relationship, Regression Chapter 6 Describe the scatterplot: 1. What is the average pattern? 2. What is the direction? 3. How strong is the relationship? 4. Identify any outliers. 1. Are the residuals normal? 2. Is there constant variability? least squares line formula: y-hat = b + mx Get OTS (t) and p-value from calculator or SPSS, Two-Quantitative Variables What do you want to know? Is there a change between the variables? Paired Data Chapter 7, One-Categorical Variable Chapter 3 Hypothesis Test np ≥ 10 AND n(1-p) ≥ 10? p comes from null hypothesis p-value = normalcdf(lower,upper,0,1)