ECN 120 Statistical Tests

Mean

Mean of grouped data

Population variance

Use N-1 for Sample Variance, for frequency tables multiply for squared deviations by the frequency before summing to find the Mean of grouped data.

Coefficient of Variation

Average Annual Growth Rate

Bayes Theorem

Binomial Distribution

P = Probability of Success

R = Number of Successes

N = Number of Trials

Binomial Approximation to E(r) and Variance of r

Poisson Distribution

Use when nP<5

Z-score

Point Estimate For Mean

Point Estimate For Proportion

Point Estimate For The Difference Between Two Means

Point Estimate For The Difference Between Two Proportions

Two Tailed Tests at 90,95 & 99%

1.64, 1.96, 2.27

Estimation With Small Samples (n<25), and unknown true variance 𝜎2

Use t-distribution, dgf either; 𝑛 - 1, 𝑛1

+𝑛2 - 2, and pooled variance for the difference between two means

When To Use A Two-Tailed Hypothsis Test

To detect any significant difference (higher or lower) from a standard- ie reject the null if smaller than the left tail or greater than the right tail

When To Use A One-Tailed Hypothsis Test

To detect a specific hypothesis that lies in one direction (greater or smaller) - ie reject the null if; Left Tail- test statistic is less than critical value, Right Tail- test statistic is more than critical value

Type One and Two Errors

Hypothesis Testing WIth Large Samples

Hypothesis Testing A Proportion

Hypothesis Testing The Difference Between Two Means

Hypothesis Testing With Small Samples (n<25)

Use t-distribution, dgf n - 1

Hypothesis Testing With Small Samples The Difference Between Two Means

Use pooled variance

When To Use A Chi-square Test

To estimate the confidence interval of a variance, To compare actual and expected frequencies

Estimating a variance: Confidence
interval

Take half the Chi square values from both the upper and lower tail, ie 0.975 and 0.025 for 95% confidence, to find the upper and lower bounds, use dgf v= n -1

Comparing Actual And Expected
Frequencies

Based on hypothesis ie null = fair die, alternative = biased die, dgf k = 1 (k is the number of possible outcomes), if the test statistic < critical Chi Square value, fail to reject, dgf contigency tables = (rows-1 X columns-1)

Testing Equality Of Two Variances

Use F-Distribution, Put the larger variance on top of the fraction so you use the upper tail only, n1 -1 = v1 (along)is always associated with the larger variance ad vice versa for n2 - 1 = v2 (down)

ANOVA

K = number of factors, n = number of observations

Correlation Coefficient

Testing The Significance Of A Correlation Coefficient

Use t-distribution, dgf n-2, if test is greater than t-value, correlation is significant

The Regression Line

𝑌 = 𝑎 + 𝑏𝑋

Goodness Of Fit

If 𝑅2 was 0.378, regression could explain 37.8% of the variance of Y

Testing The significance Of 𝑅2 Simple

Compared against F- statitsic, if test statistic is smaller then fail to reject, dgf1 = k , dgf2 = n - k - 1 (k = number of independent or explanatory variables)

Testing The significance Of 𝑅2 Multiple

Compared against F- statitsic, if test statistic is smaller then fail to reject, dgf1 = k , dgf2 = n - k - 1 (k = number of independent or explanatory variables)

Laspeyres Price Index

For the quantity index switch the places of Q and P keeping 0 and n in place

Paasche Price Index

For the quantity index switch the places of Q and P keeping 0 and n in place