hypothesis_testing Flashcards
What are the alpha levels?
- The alpha level is also known as the significance level
- The alpha level is our criterion of determining whether something is likely or unlikely
- There are 3 alpha levels:
- .05 (5%)
- .01 (1%)
- .001 (0.1%)
- Example: A significance level of .05 indicates a 5% risk of concluding that a difference exists when there is no actual difference
What is true of alpha?
- If the probability of getting a particular sample mean is less than alpha, it is “unlikely” to occur.
What are the z-scores for the following alpha levels? What is another name for these values?
- .05
- .01
- .001
These values are also known as the z-critical values
.05 = 1.65 .01 = 2.32 .001 = 3.08
What is the equation for the sample z-score (again)?
z = (xbar - mean) / (sd/sqrt(n))
What would a sample z-score of 1.82 represent in terms of alpha levels and z-critical scores?
- the z-score is greater than alpha .05 (1.65), but is not lower than 0.01 (2.32).
- So, xbar is significant at p < 0.05
For the following z-scores, what are the significance levels?
- 3.14
- 2.07
- 2.57
- 14.31
- 14 is significant at p < 0.001
- 07 is significant at p < 0.05
- 57 is significant at p < 0.01
- 31 is significant at p < 0.001
Given the following population parameters:
- mean = 7.5
- SD = 0.64
What is the z-score of the sample mean, given a sample mean of 7.13?
1) find the SE: .64/sqrt(20) = .143
2) find the z-score: (7.13 - 7.5) / .143 = -2.59
What are the two-tailed critical values for the following alpha levels:
- .05 alpha level?
- .01 alpha level?
- .001 alpha level?
- The critical regions are now on both sides of the normal distribution
- find the z-score for 97.5 since the 5% area is divided in half to find the top 2.5% and bottom 2.5%
- +/- 1.96
- find the z-score for .995 since the 1% area is divided in half to find the top .5% and bottom .5%
- +/- 2.57
- find the z-score for .9995 since the .1% area is divided in half to find the top .05% and bottom .05%
- +/- 3.32
If a sample mean of 7.13 has a z-score of -2.59, what can we say about this value with respect to a two-tailed critical value of alpha 0.05?
- The two-tailed critical values are +/- 1.96
- (-2.59) is below this threshold
- Therefore, we can say:
- It is unlikely to have gotten a mean engagement score of 7.13
- A mean engagement score of 7.13 is significant at p < 0.05
What are the z-critical values for one-tailed test and a two-tailed test?
One-tailed z-critical values:
- a = 0.05 z = 1.65
- a = 0.01 z = 2.32
- a = 0.001 z = 3.08
Two-tailed z-critical values:
- a = 0.05 z = +/- 1.96
- a = 0.01 z = +/- 2.57
- a = 0.001 z = +/- 3.27
Null hypothesis vs. alternative hypothesis?
Ho (null hypothesis): M = Mi (population parameters after intervention)
- accepting the null hypothesis means that the population parameters will be the same (not significantly different) as the population parameters after some intervention
- the sample mean will lie outside the critical region
Ha (alternative hypothesis): M < Mi; M > Mi; M != Mi
- accepting the alternative hypothesis means that the population parameters will be significantly different after some intervention
- ** the sample mean will lie somewhere in the critical region **
True or False: You can prove if the null hypothesis is true
- False
- you can only obtain evidence to reject the null hypothesis
- Example: Ho = most dogs have four legs; Ha = most dogs have less than four legs
- Sample 10 dogs and find that all have four legs.
- Did we prove that the null hypothesis is true (that most dogs have four legs)?
- No, we are simply able to NOT reject the null hypothesis and fail to accept the alternative hypothesis
How does the alternative hypothesis outcome change based on a one-tailed vs. two-tailed test?
- One-tailed: The Ha can either be M < Mi or M> Mi
- M < Mi is in the right side critical region
- M > Mi is in the left side critical region
- Two-tailed: The Ha is M != Mi which is either critical region
When do you choose a one-tailed vs. a two-tailed hypothesis test?
- one-tailed (directional): when you are attempting to predict direction
- example: when you are predicting that changing curriculum will increase student engagement
- two-tailed (non-directional): when you do not predict a direction
- typically two-tailed is chosen because it is more conservative; less likely to reject the hypothesis when it is true
- you might be wrong on the direction (decreases instead of decreases) so this helps be more certain
- one exception is when you are only concerned if something is better than the current version; then you would use one-tailed (directional)
What is the typical setup for a hypothesis test?
- Two-tailed (non-directional) test
- alpha level = 0.05
- the two critical regions are -z = -.025 and z = .025
