Hypothesis Tests

Hypothesis Tests

1. Chi-Squared Test

   • 1) Define your null and alternative hypothesis
     • Ho: There is no association between variables X and Y
     • H1: There is some association between variables X and Y
     • 2) Create an observed values table and include column totals
       • 3) Create an expected values table
         • These values come from column totals. Eg vertical column total x horizontal column total / table total
         • 4) Create a Chi-Squared values table
           • These values come from : (observed-expected)² / expected
           • 5) Add up these values to give you your test statistic
             • 6) We need to find our critical value using our significance level and degrees of freedom
               • Degrees of freedom are given by: (No of vertical columns -1)x(No of horizontal columns -1)
               • 7) Compare these values and draw your conclusion

2. Spearman's Rank Test

   • 1) Define your null and alternative hypothesis
     • Ho: There is no association between variables X and Y
     • H1: There is some association between variables X and Y
     • 2) Work out your critical value using tables
       • Use your significance level and value of n to work this out (remember to see if it is a one tailed or two tailed test)
       • 3) Compare this value with your Spearman's Rank Correlation Coefficient and make your conclusion

3. Normal Test for the Mean

   • 1) Look in the question for this information:
     • The value of n
     • 2) Define your null and alternative hypothesis
       • Ho: μ = your current mean
       • H1: μ > or < or ≠ your current mean
       • 3) Define μ
         • Where μ denotes the population mean 'insert context'
         • 4) We need to state our normal distributions
           • X~N(μ,σ)
           • x̄~N(μ,σ/n)
           • 5) Work out our test statistic which is given by: z=(x̄-μ)/(σ/√n)
             • 6) Work out our critical value which comes from inverse normal tables
               • 7) Compare these values are state your conclusion
     • The original normal distribution
     • The new mean
     • Whether we are looking for an Increase in the mean, a Decrease in the mean or just a change in the mean (telling us it is a two-tailed test)

4. Product Moment Correlation Coefficient Test

   • 1) Check the question to see if you are looking for Positive, Negative or Any correlation
     • 2) Define your null and alternative hypothesis
       • Ho: ρ = 0 There is no correlation between variables X and Y
       • H1: ρ > or < or ≠ 0 There is a positive/negative/some correlation between the variables X and Y
       • 3) Define ρ
         • Where ρ is the correlation coefficient of the parent population
         • 4) Work out the critical value taking into account the significance level and n
           • 5) Compare this to your product moment correlation coefficient and make your conclusions