NHST
What is Type I error? And does the researcher have control over Type I error?
The probability of rejecting a true null hypothesis
Yes, you can control by changing alpha
When would you use a one-sample t-test instead of a z-test?
When you don't know the population variance
What does it mean to have a between subjects or within subjects design?
Between: participants experience only one level of each factor; participants experience only one condition of the experiment
Within: participants experience every level of all the factors; participants experience all conditions of the experiment
I have a three-way ANOVA. How many IVs am I examining?
3
Scores in the general population show math proficiency scores of 100 (with population SD = 15) on a particular standardized test. Our sample scored 120 on that same standardized test. Calculate and interpret Cohen's d.
d = (120-100)/15 = 1.33
Our sample scored 1.33 standard deviations above the mean of the general population. This is a large effect.
What are 3 things you can increase to increase power?
alpha
effect size
sample size
When does the t distribution start looking more like the z distribution?
As sample size increases
What is the difference between a repeated measures and matched pairs design?
Repeated measures: the same participants are measured multiple times
Matched pairs: different participants are measured but matched on some characteristic/trait; each matched pair is compared
What does a large F statistic mean?
That the variability between groups is greater than the variability within groups
The population mean for daily studying time among students is 90 minutes. In your sample of 30 students, the mean for daily studying time is 100 minutes (sample SD = 20). Calculate the appropriate test statistic and make a statistical decision.
t = (100-90)/(20/sqrt30) = 2.74
t critical value is 2.04
Since 2.74 > 2.04, we reject the null hypothesis. On average, our sample (M = 100, SD = 20) spent significantly more time studying each day than the population (μ = 90).
What is the p value?
The probability of obtaining your results (test statistic) given that the null is true.
n - 1
You have an independent samples t-test, and want to test for significance using the confidence interval. When would you retain vs. reject a null hypothesis using the confidence interval?
Retain: If the value of 0 is in your confidence interval
Reject: If the value of 0 is not in your confidence interval
What is a source of variation in within subjects ANOVA that you don't have in between subjects ANOVA?
between-persons variation
You obtained the following for a related samples t test:
nD = 16, MD = 4, sD = 8
Calculate the 95% confidence interval and make a statistical decision.
critical t = 2.131 and sMD = 8/(sqrt16) = 2
lower: 4 - (2.131)(2) = -0.262
upper: 4 + (2.131)(2) = 8.262
95% CI [-0.26, 8.26]
Because 0 is within the confidence interval, we retain the null hypothesis.
A researcher examines whether a particular region differs in annual income compared to the national average. State the null and alternative hypotheses.
Null: Annual income in this particular region does not differ from the national average.
Alternative: Annual income in this particular region differs from the national average.
What are the 3 assumptions of a one-sample t-test?
Normality
Random sampling
Independence of observations
12% of the variance in how much people recycle (DV) was explained by political affiliation (IV).
Given that k > 2, what is the next step when you have a significant ANOVA?
A research examined 6 children's language development scores of those who went to preschool (n=3) and those who did not (n=3).
Among those who went to preschool (Group 1), the scores were: 7, 7, 8
Among those who did not go to preschool (Group 2), the scores were: 7, 7, 6
Test whether or not child language development scores differ between groups using a .05 level of significance. Calculate the test statistic and make a statistical decision.
Group 1 Mean = 7.33
Group 1 Variance = [(49+49+64) - (222/3)]/(3-1) = (162 - 161.33)/2 = .33
Group 2 Mean = 6.67
Group 2 Variance = [(49+49+36) - (202/3)]/(3-1) = (134 - 133.33)/2 = .33
Pooled sample variance = (.33+.33)/2 = .33
Estimated standard error: sqrt[(.33/3) + (.33/3)] = .47
t = (7.33 - 6.67)/.47 = 1.40
t critical value = 2.776
Because 1.40 is less than 2.776, we retain the null hypothesis. There is no significant difference between the two groups.
What do we mean by "significance"/"statistical significance"?
A decision about the null hypothesis.
When a null hypothesis is rejected, results are significant.
When a null hypothesis is retained, results are not significant.
Given that all other values remain the same, if the estimated standard error were to increase, would you be more or less likely to reject the null hypothesis
Less
Increasing the ESE would lead to a lower test statistic value, this decreasing the probability of rejecting the null hypothesis
In a related samples t-test, what is a key step you have to do to calculate the test statistic that you don't do when calculating an independent samples t-test?
Calculate the difference scores
Researchers conducted a one-way between subjects ANOVA and got the following results: F (2, 67) = 6.12, p < .001. What was the sample size?
N = 70
Because for one way between subjects ANOVA:
Total df = between groups df + within groups df
and Total df = N - 1
The following is from an incomplete F table summarizing results from a study examining life satisfaction among unemployed, retired, part-time, and full-time employees. Calculate the test statistic and make a statistical decision.
MS between groups = 16
Within groups df = 36
Total SS = 128
Between groups df = k - 1 = 3
Between groups SS = (16x3) = 48
Within groups SS = Total SS - SSBG = 128 - 48 = 80
Within groups SS = 80/36 = 2.22
F = 16/2.22 = 7.21
Critical value for F (3, 36) = 2.87
Because our obtained test statistic is greater than the critical value, we reject the null hypothesis.