One Sample t Test
Determine the degrees of freedom for a one sample t-test.
df = n - 1
Determine the degrees of freedom for an independent samples t test.
df = n1 + n2 - 2
State the degrees of freedom for a related samples t-test.
Which statement is indicative of the meaning of the null hypothesis?
A) any difference observed between two means is GREATER than what is expected by chance
B) any difference observed between two means will be due to chance
C) any difference observed between two means will be due to something other than chance
D) none of the above
B) any difference observed between two means will be due to chance
Hypothesis tests require decisions to made about:
A) the research hypothesis
B) the alternative hypothesis
C) the null hypothesis
D) none of the above
C) the null hypothesis
Which of the following is an example of an alternative hypothesis (Ha) for a one sample t-test?
A) μ = 82
B) μ ≠ 82
C) μD = 0
D) μD ≠ 0
B) μ ≠ 82
Indicate the independent and dependent variables in the following study: Dr. Brenda wanted to determine if reaction time in individuals who got little sleep differs from reaction time in individuals who got a good night's sleep.
100 bonus points if you correctly define independent and dependent variable.
independent variable: amount of sleep
dependent variable: reaction time
Bonus:
independent variable: the experimentally manipulated variable; the cause
dependent variable: the variable that is measured; the effect
Which of the following is an example of a null hypothesis for a related samples t-test?
A) μ ≠ 82
B) μ = 82
C) μD = 0
D) μ1 - μ2 = 0
C) μD = 0
What type of error are you making when you observe a relationship that does NOT exist?
Type I error
Under what circumstances is a t-statistic used instead of a z-score for a hypothesis test?
A) When σ is large
B) When σ is small
C) When σ is known
D) When σ is unknown
D) When σ is unknown
What does sM represent? Write the formula for sM.
sample standard error of the mean; sM = s / √n
Which of the following is NOT an assumption of the use of the independent samples t-test?
A) each sample of observations is independent of the other sample
B) the scores of one group are not related to the scores of the other group
C) the scores from one group are correlated with the scores of the other group
D) samples come from a normally distributed population
C) the scores from one group are correlated with the scores of the other group
What is the numerator of tcalc for a related samples t-test? How can we calculate this value?
MD; MD = ΣD / n
What type of error are you making when you observe no relationship when one actually exists?
Type II error
If tcalc is less than tcrit, what decision do we make about the null hypothesis? What does this tell you about the significance of the result? How does p compare to alpha?
fail to reject H0; not significant; p > alpha
Fill in the blanks: a one sample t-test aims to compare the means of a __________ and a ______. Therefore, the numerator of tcalc in a one sample t-test is ______.
population; sample; M - μ
H0: μ1 - μ2 = 0
H1: μ1 - μ2 ≠ 0
Give an example of a study in which we would apply a related samples t-test.
self-esteem measured after a period of positive affirmations and then after a period of negative affirmations
Which of the following is a Type II error?
A) failing to reject the null hypothesis when it is false
B) rejecting the null hypothesis when it is true
C) concluding that a treatment has no effect when it really does
D) both A and C
D) both A and C
Fill in the blanks: While Cohen’s d is a measure of the direction of the difference between means, _____ is a measure of the _____ of that difference, or the magnitude of that difference.
List all the interpretations of the values of Cohen's d and r2.
r2; extent
d: .2 -> small effect, .5 -> medium effect, .8 -> large effect
r2: .01 --> small effect, .09 --> medium effect, .25 -> large effect
Write out the procedure for a one sample t-test and include any necessary formulas under each step.
1. State the hypotheses, degrees of freedom, and set alpha.
2. Calculate sM, the standard error of the mean.
3. Calculate tcalc and compare it to tcrit
4. Calculate effect size, both d and r2
5. Write a statistical summary statement, including the means, standard deviation, t(df) = _, and effect sizes.
List the procedure of an independent samples t-test and include all the relevant formulas under each step. Be sure to state what each symbol represents (for instance, if you say that s = . . ., be sure to say that s = sample standard deviation, etc).
1. State the hypotheses, degrees of freedom, and alpha.
2. Find the sums of squares for both groups (SS1 and SS2)
3. Calculate pooled variance, sp2
4. Calculate the standard error of the difference between sample means, sM1-M2
5. Calculate tcalc and compare the value to tcrit
6. Calculate effect size, both d and r2.
7. Write a conclusion statement and include the means of both groups, t (df) = __, and the values of d and r2.
List the procedure of a related samples t-test and include all the relevant formulas under each step. Be sure to state what each symbol represents (for instance, if you say that s = . . ., be sure to say that s = sample standard deviation, etc).
1. State hypotheses and degrees of freedom and set alpha.
2. Calculate D, the difference between means, and D2 for each score. Also, calculate ΣD and ΣD2.
3. Calculate sD, the standard deviation of differences.
4. Calculate sMD, the standard error of mean differences.
5. Calculate tcalc and compare it to tcrit.
6. Calculate effect size, both d and r2.
7. Write a statistical summary statement, including t(df) = _ and the value of d and r2.
Fill in the blanks: If you reject the null hypothesis when it is true, you have made a _______ error, which means you found _______ when there is none.
Type I; significance
As the value of tcalc increases, what happens to the probability, p?
the value of p decreases