Hypothesis Testing

Which test do you use if you are testing for a correlation?

Which test do you use if you are testing for a correlation?

PMCC test

Which test do you use if you are testing for an association?

SRCC test

Which test do you use if you are testing for an association and have data in a contingency/two way table?

Chi Squared Test

Which test do you use if you are comparing the mean to a given value?

Normal Z Distribution

Which tests do you use if you are comparing the population average of two paired samples?

Paired sample Wilcoxon Signed Rank

Paired sample Sign Test

Which tests do you use if you are comparing the population average to a given value?

Single sample Wilcoxon Signed Rank

Single sample Sign Test

Which test do you use if you are comparing the population difference of two non-paired samples?

Wilcoxon Rank Sum

Define a Type I error

Reject H₀ when it is true

What is the probability of a Type I error?

The same as the significance level

Define a Type II error

Accept H₁ when it is false

What is the Central Limit Theorem?

If n >30, then we can find probabilities about a mean even if the original distribution wasn’t a normal distribution

Define the term parameter

A numerical value of a population

Define the term statistic

A numerical value of a sample

What assumptions about the distribution are required for the sign test to be valid?

No assumptions

What assumptions about the distribution are required for the Wilcoxon signed rank test to be valid?

• distribution is symmetrical

• distribution of differences is symmetrical for a paired test

What percentage of data lies within one standard deviation of the mean in a normal distribution?

68%

What percentage of data lies within two standard deviations of the mean in a normal distribution?

95%

What percentage of data lies within three standard deviations of the mean in a normal distribution?

99.8%

What must you do to the data before you can calculate the SRCC value?

Rank the data

What are H0 and H1 for a SRCC test?

H0: no association between x and y

H1: positive/negative/some association between x and y

What are H0 and H1 for a PMCC test?

H0: p = 0

H1: p > 0 or p < 0 or p doesn’t equal 0

When do we reject H0 in SRCC and PMCC tests for POSITIVE correlation/association?

If the test statistic is ABOVE the critical value

When do we reject H0 in SRCC and PMCC tests for NEGATIVE correlation/association?

If the test statistic is BELOW the critical value

What are H0 and H1 for the Chi squared test?

H0: no association between x and y

H1: positive/negative/some association between x and y

When do we reject H0 in the Chi squared test?

When the test statistic is ABOVE the critical value

What are H0 and H1 for the Normal Distribution (z) Test?

H0: u = value

H1: u > value or u < value or u does not equal value

What are the steps for the Normal Distribution (z) test?

• H0 and H1

• test stat = value of x bar

• reject H0 if the p value is ABOVE the critical value

What are H0 and H1 for the Wilcoxon Rank Sum test?

H0: nd = 0

H1: nd > 0 or nd < 0 or nd does not equal 0

What assumption do you make with the Wilcoxon Rank Sum test?

the population is symmetric

What are the steps for the Wilcoxon Rank Sum test?

• H0 and H1

• Rank data across both sets

• Total of ranks for each set

• Calculate U values

• Test stat = smallest U value

• Critical region is anything less than or equal to critical value

• Reject H0 if test stat is ABOVE critical value

When do you need to pool data for a Chi squared test?

If any of the EXPECTED values are less than 5