psych 280 exam 2
What is the critical value that we use for testing the null hypothesis, with α = .05?
1.96
What are the assumptions of a single sample z-test? What are some examples of violations of each of the assumptions?
1.Random (representative) Sampling 2.Independent Observations 3.Constant σ across groups 4.Distribution of Sample Means is Normal
If the null hypothesis is true, what percent of sample means will fall within +/- 1.96 standard errors of the mean?
95%
What percent will fall within +/- 2 standard errors of the mean?
95.4%
What percent will fall within +/- 2.58 standard errors ?
99%
What percent will fall within +/- 3.30 standard errors?
99%
What is an alternative hypothesis?
: Ha or H1 predicts that there is an effect, there is a difference
A researcher fails to reject a null hypothesis that is false. What happened?
A Type II error
What does alpha refer to?
Alpha level refers to the level of significance for the hypothesis test. The alpha () value is a small probability that is used to identify the low-probability samples. In other words, alpha level is a probability value that is used to define the concept of "very unlikely" in a hypothesis test (how unlikely is it to obtain this value or something lower for our test statistic? If very unlikely, aka less than 5% chance, we reject Ho)
Why do we use a pooled variance for the two sample t-test?
Because if H0 is true, there is only 1 population, thus only 1 population variability. The reason the 2 sample variations look different is just due to sampling error. To get the best guess at the true population value, we put the variability measures from the 2 samples together, weighting or putting more trust in the value from the larger sample
Why do we have to use degrees of freedom for a t-test?
Because we are estimating the population SD from the sample SD. The sample SD is always smaller than the population SD so we correct for it.
Why are hypotheses written in terms of population parameters and not sample statistics?
Because we want to test sample(s) to infer the population(s) of interest. We want to make a conclusion about the population(s). Therefore, we write in population parameters instead of sample statistics.
What are the differences between a Between-Subjects design and a Within-Subjects design?
Between-subjects design = each participant goes through only one condition of the study (each person watches only 1 TV show) Within-subjects design = each participant goes through all the conditions of the study (each person watches all 3 TV shows)
How do you use a t-table to decide if a sample mean differs significantly from a population mean?
Calculate the obtained t and compare it to the critical value that is associated with the df of your sample
What are the values given in a t-table? What do they represent?
Critical values, df, and alpha levels.
Which type of t-test is appropriate for a Within-Subjects design?
Dependent/Related/Paired samples t-test
What is a Type II error, and how does it relate to a Type I error?
Fail to reject the null when in reality the null is false. Type I and Type II error are inversely related. As you decrease the probability of a Type II error, you increase the probability of a Type I error.
What is a null hypothesis?
Ho predicts no effect, no difference
If the null hypothesis is true, what percent of sample means will be greater than 1.96 standard errors of the mean? What percent will be lower than 1.96 standard errors?
If the null hypothesis is true, 2.5% of the sample means will be greater than 1.96 SE and 2.5% will be lower than 1.96 SE of the population (or sampling distribution) mean.
How are difference scores used in a Within-Subjects design?
In a within-subjects design, the difference score is the difference between the score that a participant has at one level and at another level of IV.
What is the effect of n on the standard error of the mean?
Increasing sample size will decrease standard error. As the denominator of this formula gets bigger, the value for standard error gets smaller. As you increase sample size, the error of your estimate gets smaller, which increases the trustworthiness of the mean. You can feel more confident in your estimate as the sample size increases.
What are the assumptions of a single sample t-test?
Independent observations distribution of scores in the population is normal
Which type of t-test is appropriate for a Between-Subjects design?
Independent samples t-test
What are the primary advantages of a Within-Subjects design?
Need less participants (especially good for studying rare populations) Each participant serves as their own control, decreases between subjects variability
What are degrees of freedom?
Number of values that are free to vary. n-1
What is the difference between a one sample t-test and a one sample z-test?
One sample t-test is used when we don't know the population SD
What are the disadvantages of a Within-Subjects design?
Order effects are a disadvantage, when scores may be systematically related to the order in which the participant takes the test
What does Cohen's d assess?
Practical significance
What is a Type I error, and how does it relate to the alpha level?
Reject the null when in reality the null is true. There is a alpha% chance you will make this type of error.
How do you calculate the standard error of the mean if you don't know σ?
S/square root of n
How do you calculate the standard error of the mean (i.e. a single mean) if you know σ?
SD/square root of n
Be able to calculate the standard error of the mean, assuming you know σ
SE of mean= SD/sqroot of n
Be able to calculate the standard error of the mean, assuming you don't know σ.
SE of mean=s/sqroot of n
What are the differences between a single sample t-test and a two-sample t-test?
Single sample t-test only has one sample which is being compared to a known population mean. A two-sample t-test does not involve any known parameters.
A researcher is interested in whether coaching can increase IQ scores. It is known that the mean IQ in the population is 100, with a standard deviation of 15. A sample of 36 participants is randomly chosen, and provided with the coaching program. After the program, the mean IQ in this sample is 115. The researcher wishes to perform a statistical test to see if the coaching had an effect. What type of test should be performed? What are the degrees of freedom for this test?
Single sample z-test Degrees of freedom don't apply because we are doing a z-test
What is a standard error? How does it relate to a standard deviation?
Standard error is the standard deviation of a sampling distribution of all possible sample means from samples size n. In other words, it is the average distance from the mean of a sampling distribution having samples size n (or the population mean bc CLT)
When doing hypothesis testing, why do researchers typically use alphas of .05, .01, or .001?
There is a very low probability of obtaining a sample mean in those regions. We don't typically want to be wrong more than 5% of the time. In other words, we are OK with being 95% or more confident in our decision
Why do we have two sources of error when calculating the standard error for a two sample t-test?
There is sampling error in two samples now because we are estimating two population means
How can I decrease Type I and Type II errors simultaneously?
To decrease both, increase power- increase n
If we reject a null hypothesis when it is true, what kind of error have we made?
Type I
What are "order effects"?
a disadvantage, when scores may be systematically related to the order in which the participant takes the test
Which of the following is an example of a repeated measures design?
a teacher compares pre-test and post-test scores for a sample of students
What is homogeneity of variance?
assumes that the variability of scores is the same in 2 different groups/levels/treatments (same SD's) and there's only a difference between means.
Why is it important to evaluate "practical significance" in addition to "statistical significance"?
because it is easy to reject a null - just get a huge sample, so we need to know how important this finding is in real life
What are the cutoffs for "small", "medium", and "large" effects, according to Cohen's d?
d=0.2: small effect d=0.5: medium d=0.8: large
How do I decrease my probability of making a Type I error?
decrease alpha but this increases the probability of a Type II error
Which of the following make it more likely that a researcher can reject a null hypothesis?
increase n
Which of the following will increase the "power" of a statistical test?
increase n
What happens to the standard error of the mean as n decreases?
it increases
Assume a researcher conducts a one-sample z-test, and obtains a z = 1.52. Assume she wants to use a conventional level for α. Can she reject HO ?
no
What is an obtained t?
our calculated test statistic -must exceed critical t to reject Ho.
What does it mean to say that a result is "statistically significant"?
p<alpha
What does r2 evaluate?
proportion of variance in the DV accounted for by the IV.
What are the cutoffs for deciding whether an effect is "small", "medium", or "large" according to the r2 value?
r^2=0.01: small r^2=0.09: medium r^2=0.25: large
A new diet is developed to decrease cholesterol levels in adults at risk of developing heart disease. The mean cholesterol level in the patient population is 200. A sample of 50 patients tries the new diet, and after 3 months, the mean cholesterol is M = 192, with s = 21. What type of statistical test should be performed?
single sample t-test
Assume a researcher wishes to compare a sample mean from one group with a known population mean. Assume the researcher also knows the value of the standard deviation of scores in the population. Which analysis should be performed?
single sample z-test because we have one group and we know pop mean and SD of scores
What goes into the denominator of a t-test?
standard error
What is a critical region?
the area at which we determine we should reject Ho because the probability of a test statistic to fall into this area is extremely low.
What is a Difference Score?
the difference between the scores in 2 levels of IV
What does a z for a sample mean represent? How does a z differ from a t?
the number of standard deviations away from the population. t depends on the degrees of freedom, z does not. t is a thicker distribution (has thicker tails) t is an estimate, because you don't know the population parameters (therefore we correct for t using an underestimate of the true population variability by using a critical t that is greater than a critical z, based on the number of participants in the sample).
A medical researcher is working on a new treatment for a certain type of cancer. The average survival time in the population, after diagnosis, is two years using the standard treatment. After trying a new treatment on three patients, she observes an average survival time of four years. Even though survival has doubled, the result is not statistically significant at the .05 level. Which of the following is the most likely explanation for the non-significant result?
the sample was too small to detect a significant difference
What is a critical t?
the value at which we evaluate whether we should retain or reject Ho by comparing it to the obtained t. Figure out by having df and alpha level (alpha level typically at .05)
Which of the following is a null hypothesis?
u=50
What is "counterbalancing"?
using all of the possible orders of conditions to control order effects
What is the difference between σ and s?
σ: standard deviation of a population s: standard deviation of a sample
