t-Tests

• t-test used to determine if there’s a difference between two means
• One sample t-test: difference between sample mean and population mean (difference between x and u)
• Is there a difference in SAT scores between Californians and Americans?

  One-sample t test
• Dependent-samples t test: Difference between 2 samples that are related to each other; also known as paired or related-samples t test
• Is there an increase in performance before and after academic intervention?

  Dependent-samples t test
• Independent-samples t test: Difference between 2 samples that are unrelated to one another
• Is there a difference in test performance between those who did and did not have academic intervention?

  Independent-samples t test
• As the numerator gets bigger, the value gets bigger
• As the denominator gets smaller, the value gets bigger
• Is 8/1 bigger than 4/1?

  Yes
• Is 4/1 bigger than 2/1?

  Yes
• Is 4/1 bigger than 8/1?

  No
• Is 1/2 bigger than 1/8?

  Yes
• Is 1/8 bigger than 1/2?

  No
• Degrees of Freedom in One-sample t test?

  df=n-1
• Degrees of freedom in dependent-samples t test?

  df=n-1
• Degrees of freedom in a independent-samples t test?

  df=n-2
• In the table of critical values: as you increase sample size, you decrease critical value
• How many participants are included in a one-sample t test with these results; t(29)=2.02,p>.05?

  30
• How many participants are included in a dependent-sample t test with these results; t(29)=2.02,p>.05?

  30
• How many participants are included in a independent-sample t test with these results; t(82)=2.02,p<.05?

  84
• How many sample scores were analyzed in a one-sample t test with these results; t(29)=2.02,p>.05?

  30
• How many sample scores were analyzed in a dependent-sample t test with these results; t(29)=2.02,p>.05?

  60
• How many sample scores were analyzed in a independent-sample t test with these results; t(82)=2.02,p<.05?

  84
• In a one-sample t test with these results; t(29)=2.02,p>.05, is there a difference between the means with alpha of .05?

  No difference because chance of making a T1 error by rejecting H null is more than 5%.
• In a dependent-sample t test with these results; t(29)=2.02,p>.05, is there a difference between the means with alpha of .05?

  No difference because the chance of making a T1 error by rejecting H null is more than 5%.
• In a independent-sample t test with these results; t(82)=2.02,p<.05, is there a difference between the means with alpha of .05?

  Yes, there is a difference because the chance of making a T1 error by rejecting H null is less than 5%.
• If p is more than .05 (p>.05), do you reject the H null?

  No, don’t reject H null
• If p is less than .05 (0<.05), do you reject the H null?

  Yes, reject H null
• Values between -2 and +2 for skewness and kurtosis are acceptable for a normal univariate distribution
• When you’re testing assumptions you don’t want p to be less than .05. If p is less than .05, it’s saying that the assumption was not met
• heterogenous variance: spread of scores in one population is different from the other population

  
• homogenous variance: both spread of scores is equal to each other

  
• All of these represent homogenous variance

  
• What is effect size?

  measure of size of a relationship between variables
• Effect size informs if a statistically significant result is meaningful
• “You develop a drug that lowers anxiety by only .001%. Is this significant?” Is a question of?

  Effect size
• Cohen’s d is a common measure of what?

  Effect size for t tests
• <.2 (less than .2) effect size?

  Trivial effect size.
• >.2 and <.5 (between .2 and .5) effect size?

  Small effect size