FM - Unit 2 Flashcards
(22 cards)
Discrete Random Variable - Combinations of 2 < terms
E(ax + b) = aE(x) + b
Var(ax + b) = a²Var(x)
Discrete Random Variable - Combinations of 2 < variables
E(ax + by) = aE(x) + bE(y)
if x & y are independent:
E(xy) = E(x)E(y)
Var(ax±by) = a²Var(x) + b²Var(y)
Continuous Random Variable - Cumulative Distribution
₀∫ˣ f(x) dx = F₁(x) + … + Fₙ(n)
where Fₙ(x), a < x < n
etc
Poisson Characteristics
Random
Independent
Constant rate
Binomial Characteristics
Two outcomes
Independent
Constant probability
Median From Cumulative Frequency
Median = m, where F(m) = 0.5
Chi-Squared Statistic - p-value
Probability that results observed will be those used to get it under the null hypothesis.
Can be used instead of critical values with significance levels if given (if smaller than significance level, significant ALWAYS).
Chi-Squared Statistic - Degrees of Freedom
(w-1)(h-1) - 1 for however many estimated values (like p)
Chi-Squared Statistic - Pooling
If the expected frequency is less than 5, the categories must be pooled.
Goodness of Fit Test - Hypotheses
H0 : [Model] IS an appropriate model for the dataset
H1: [Model] is NOT an appropriate model for the dataset
Chi-Squared Statistic - Goodness of Fit or Chi-Squared Test
Goodness of Fit gets its expected values from the distribution that is being checked. Uses chi-squared statistic (if chi-squared is more than critical value, significant).
Chi-Squared Test gets its expected values from the totals of the observed values.
Purpose of Statistical Models
To forecast results from a set of data
To describe real world situations
Least Squares Regression Line Limitations
Can’t rearrange to find x from y
Extrapolation outside of tested range is inaccurate
Relationship may not be linear
When Is Test Statistic > Critical Value Significant?
Chi-squared test
Goodness of fit test
Any correlation test
When Is The Null Hypothesis Positive?
Goodness of fit test
Mean Value When >1 p.d.f
Add the individual mean values
Comparing Chi-Squared Statistics In Association Test
Smaller values imply a weaker association
Must have equal d.o.f, if not use p-values instead.
Comparing Chi-Squared Statistics In Goodness of Fit Test
Smaller values imply aggreement with null hypothesis
Must have equal d.o.f, if not use p-values instead.
Exponential Distribution
Models the waiting times between poisson events.
Is memoryless, time before the next event is independent from the time already having waited.
(P(x > t + s) = P(x > s))
When Should Spearman Be Used In Place of Pearson?
Data is ordinal
Data is not in a linear relationship
Data is not in a bivariate normal distribution
Hypotheses
p = 0
p =/0
Only for pearson correlation test
Binomial Approximation
Poisson can be used if n is large and p is small
