Please enable JavaScript.
Coggle requires JavaScript to display documents.
Inference for Quantitative Data - Coggle Diagram
Inference for Quantitative Data
Confidence Interval for Pop. Mean
Matched pairs
Samples/experiments which treatments are carried out on the same person
T-distribution
Symmetirc/bell-shaped but have more area on its tails
t-test:
Degrees of Freedom
Defines the t-distribution. (df = n – 1)
As the degress of freedom increase, the distribution approaches normal density curve
Constructing a Cl (use 4-step plan)
Conditions(Plan)
Independence
: 10% condition when random sampling; Random assignment - what's being measured is independent
Normality
: CLT (n>=30), If CLT is not met graph your sample data(note no sever skew or outlier) than assume normal
Randomness
: Random sampling/Random assignment
If all conditions met, do a 1-sample t-interval
Standard error equation:
CI equation:
Interpretation: We are (Confidence level) confident that the interval (Confidence Interval) captures the true mean of (context).
t-critical: invT(area = (1-CI)/2, df)
Calculator: 1-sample t-int
Significant Test for a Pop. Mean
Conditions
Independence
: 10% condition
Normality
: CLT (n>=30), If CLT is not met graph your sample data(note no sever skew or outlier) than assume normal
Randomness
: Random sampling/Random assignment
If all conditions met, use 1-sample t-test
Construct a 4 step plan
Plan
: Check if the conditions are met
Do
: t-test:
p-value = tcdf(LB, UB, df)
State
: Ho/Ha
Conclude
: Compare p-value and significance level to check whether H0 is rejected and do we have convincing evidence for Ha
Calculator: 1-sample t-test
If its a matched pair experiment for 2 samples, we use 1-sample t-test for its significance test
Confidence Interval for the Diff. Of Two Means
4-step plan
Plan
Randomness
: Random sampling/Random assignment
Independence
: 10% condition for both dist.
Normality
: CLT met for both n, or both dist have to have no severe skew or outliers
If all conditions met use 2-sample t-interval
Conclude
We are (Confidence level) confident that interval (Confidence Interval) captures the true mean difference of (context).
If 0 is included in the interval we have convincing evidence that both distribution are the same
State
Define variables & your task
Do
Df Equation:
Use technology to find Df
Confidence Interval Equation
:
Caculator
: 2-sample t int
Significance Tests for a Diff. In Means
4-Step Plan
Plan
Normality
: CLT met for both n, or both dist have to have no severe skew or outliers
Independence
: 10% condition for both dist.
Randomness
: Random sampling/Random assignment
If all conditions met use 2-sample t-test
State
Define your varibales and Ho/Ha
Do
t-stats:
p-value = tcdf(LB, UB, df)
Calculator
: 2-sample t-test
Conclude
Compare p-value and significance level to check whether H0 is rejected and do we have convincing evidence for Ha
