Introduction to Independent-Samples t-tests
- 2. Descriptive vs. Inferential Descriptive Statistics Describe the data Examples: mean & standard deviation Inferential Statistics Generalize to the population Examples: z-tests & t-tests μ = population mean
- 4. Sampling Theory Theoretically we would pull infinite samples out of a population to construct a distribution called the sampling distribution Taller and thinner normal curve The standard deviation of the distribution sample is called the standard error of the mean (SEM) The SEM when conducting an independent samples t- test is called the standard error of the difference (SED)
- 5. T-test In this class we are going to look at the t- distribution It is different from the z-distribution in 2 ways: Adjusts based on sample size Use a t-test when a population standard deviation is unknown
- 6. 3 Types of T-tests One-Sample T-test Compare the mean to a population mean Population standard deviation is not known Hypotheses: H0: μ V (or ≤ μ - V 0) ≤ Ha: μ> V (or μ- V > 0)
- 7. 3 Types of T-tests Related-Samples T-test Compare two means from the same group Compare the difference between two means to 0 μd is the difference between the two means H0: μd 0 (or ≤ μd - 0 0) ≤ Ha: μd > 0 (or μd - 0 > 0)
- 8. 3 Types of T-tests Independent-Samples T-test Compare two means from two different populations No information about the population One-tailed hypothesis H0: μ1 ≤ μ2 (or μ1 - μ2 0) ≤ Ha: μ1 > μ2 (or μ1 - μ2 > 0) Two-tailed hypothesis H0: μ1 = μ2 (or μ1 - μ2 = 0) Ha: μ1 ≠ μ2 (or μ1 - μ2 ≠ 0)
- 9. Independent-Samples In a one sample t-test we are trying to determine if the samples we are looking at came from a particular population What if we are trying to determine whether two samples came from the same population or from two different populations How do we do this?
- 10. Hypotheses Testable statements We have two hypotheses in stats: Null hypothesis Indicates no effect or that the two samples came from the same population Represented by H0 Alternative hypothesis This is the claim that is being made Represented by Ha
- 11. Hypotheses Null hypothesis Will only ever use or = ≤ ≥ Example: H0: μ1 ≤ μ2 or μ1 - μ2 0 ≤ Alternative hypothesis Will only ever use < > or ≠ Example: Ha: μ1 > μ2 or μ1 - μ2 > 0 The null and alternative hypotheses will always have opposite signs
- 12. Probability Alpha (α) Probability of generating a false-positive (reject the null when we shouldn’t have) Probability that an event occurred by random chance We will always set our alpha to .05 for this class and test against that (industry standard)
- 13. T Values Tobtained Difference of two means converted into standard error units Tcritical Fixed value on the curve associated with alpha We compare Tobt to this value to determine statistical significance
- 14. Tobt Equation Converts the difference of the two means into standard error units which have a probability associated with them
- 15. Compare Tobt and Tcrit Remember, Tcrit separates 95% of the values in the distribution from the remaining 5% (α = .05) Tobt is a calculated standard error score associated with the probability our event has occurred by chance If Tobt is farther from the mean than Tcrit then we can reject the null and we have support for our alternative hypothesis This means it is unlikely that the two samples came from the same population – the two samples are statistically different
- 16. Take Home Message If Tobt falls in the reject region marked off by Tcrit (if Tobt is further away from 0 than Tcrit) reject the null (H0). If we reject H0 the results are significant and p < .05 If Tobt does NOT fall in reject region (if Tobt is closer to 0 than Tcrit) we FAIL to reject the null. If we fail to reject H0 the results are not significant, p > .05 Tcrit Reject region
Editor's Notes
- #8: This is the type of test we will be doing in this class.