Psych Research Methods II Exam I

What is the logic of hypothesis testing?

o   We look for the likelihood that our data are consistent with the idea that there is no effect

·   What kinds of statistical procedures are used for hypothesis tests?

o   T-test, chi-squared, ANOVA

·   How do null and alternative hypotheses differ, and what is the goal of the researcher for each?

o   The null is no effect, and the alternative is there is an effect; you want to retain the alternative and reject the null

·   What are the steps involved in hypothesis testing?

o   State null and alternative hypotheses

o   Determine characteristics of null

o   Calculate appropriate test statistic

o   State decision about whether null was rejected

o   State the conclusion verbally in terms of finding and variable names

·   How can the logic of hypothesis testing be presented graphically using distributions?

o   Plot the relevant populator parameter under the null hypothesis as a bell-shaped curve, then visually mark where your sample statistic falls on that curve

What is the difference between one-tailed (directional) versus two-tailed (non-directional) tests?

o   One tailed goes in a specific direction where as two tailed can go in either direction

·   When we reject or fail to reject a null hypothesis, in what ways may that decision be inaccurate?

o   If we fail to reject when the null was false (Type I), or we reject when null was true (Type II)

·   What is the trade-off in setting alpha at .05?

o   Reducing the risk of type I error increases the risk of type II error

·   What are common misunderstandings in what the p-value provides?

·   1.Probability that the null hypothesis is true
2.Probability that a finding is “merely a fluke”
3.Probability of falsely rejecting the null hypothesis
4.Probability that replicating the experiment would
not yield the same conclusion
5.Probability that the alternative hypothesis is true
6.The alpha level of the test is determined by the
p-value
7.Indicates the size or importance of the observed
effect

·   What are some of the common misunderstandings and controversies in hypothesis testing?  What are suggested solutions?

o   Logic is unintuitive

o   Research scientists commonly misunderstand what they are actually doing when using hypothesis testing

o   Type 1 error rates inflated

o   Fixed with: Confidence intervals, effect sizes, Bayesian theory

·   What kinds of information does probability provide?

o   Quantify uncertainty

o   Inform odds of specific scores occurring

o   Information about what will happen in the long run

·   How is probability theory useful in the field of psychology?

o   Diagnoses

o   Risk

o   Relationship between variables

o   Likelihood of behavior

·   What is the multiplication rule and how is it used?

o   Used when events are independent by multiplying the two probabilities together

·   What is the addition rule and how is it used?

o   Used when events are mutually exclusive by adding the events together

·   Definitions

o   Hypothesis testing

§  The process of determining whether data support your prediction

o   Inferential tests

§  Hypothesis tests and t tests

o   null vs. alternative hypotheses

§  there is no effect v.s. there is an effect

o   one-tailed (directional) vs. two-tailed (non-directional) tests

§  predict specific direct v.s. no direction predicted

o   type I & II errors

§  False positive (reject the null when null is true)

§  False negative (fail to reject the null when null is false)

o   p-value

§  probability of obtaining a test statistic at least as extreme as the one that was actually observed, given that the null hypothesis is true

o   alpha, region of rejection, & critical value

§  significance level, range of values for test statistic that would lead to rejecting the null, boundary point between region of rejection and acceptance

o   probability theory

§  Study of likelihood and uncertainty

o   multiplication rule

§  probability of one outcome AND another

o   addition rule

§  Probability of one outcome OR another

The Central Limit Theorem and the z-test (Lecture, activities, & PsycLearn G)

·   When do we use the z-score?

o   Test for the null hypothesis of a single sample when you know the population variance

·   What is the standard normal curve and how is it used?

o   Mean of 0 and STDEV of 1 which is used in statistics to standardize data from different sets

·   How do we calculate a z-score?

o   Subtract the mean from a data point and then divide the result by the standard deviation

·   What is the difference between the z-score and the z-test?

o   Comparing a single score versus sample of scores

·   What does it mean that the z-test is a parametric test that is inferential?

o   Makes estimations about population characteristics that allows for inferences about population based on a sample

·   Why do we compare our obtained z-statistic to a sampling distribution instead of a population distribution of scores?

o   It represents the theoretical distribution of possible sample means that could be obtained from a population

·   How do we find the standard error of the mean?

o   Divide the sample standard deviation by the square root of the sample size

·   What is the central limit theorem and why is it useful?

o   The sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough

·   What are possible research hypotheses for a one-directional z-test?

o   Stated above or below

·   How do we calculate a one-directional z-test?

o   Probability that a sample mean is found in this sampling distribution and that 5% or less chance that our mean came from the sampling distribution

·   How is calculating a two-tailed z-test different from a one-tailed z-test?

o   Divide alpha of 5% between the two tail ends of the distribution

·   Definitions

o   z-score

§  Compare a single score to a population

o   z-test

§  Compare a sample of scores with a population

o   sampling distribution of the mean

§  the mean of the population from which scores were sampled

o   standard error of the mean

§  standard deviation of the sampling distribution

o   central limit theorem

§  A distribution of sample means approaches normality as N increases

The one-sample t-test (Lecture, activities, & PsycLearn H)

·   How do the z-test and the one-sample t-test differ?

o   Population standard deviation is known versus unknown

·   When would we use the one-sample t-test?

o   Compare the mean of a single sample to a known or hypothesized population mean

·   What are degrees of freedom and based on what are they calculated?  How does this relate to the fact that the t-distribution is a family of distributions?

o   “free” data points (n-1)

·   What are the features of the t-distribution and how are these different from those of the z-distribution?

o   Higher N

o   Higher dg

o   Less variability

o   Less extreme critical values

o   Need less extreme t-value to have a significant effect

·   What is the logic of the t-statistic?

·   ` determine if there is a significant difference between the means of two groups and how they are related

·   How do we calculate a one-sample t-test?

o   “difference in values”/”natural variability”

·   Definitions

o   population variance estimation

§  statistical process of using a sample from a population to calculate an approximation of the true “population variance”

o   t-distribution

§  A collection of sampling distributions in which there is a different distribution for each sample size

o   one-sample t-test

§  A hypothesis test used to compare a sample mean to a population mean when the population standard deviation is not known

The paired-samples t-test (Lecture, activities, & PsycLearn I)

·   When do we use the paired-samples t-test?

o   When you want to compare the means of two related samples

·   What are two different reasons to use the paired-samples t-test?

o   Repeated measures

o   Matched samples

·   What are repeated measures (or within-subjects) designs, and what are their benefits and shortcomings?

o   Benefits

§  Participants act as their own control

§  Need fewer participants total to achieve sufficient statistical power, because same ps are in each condition

o   Shortcomings

§  Ps might figure out what variable is being manipulated

§  Practice effects

§  Longer studies

·   What is the logic behind the calculations for the paired-samples t-test?

o   Difference is calculated to control for individual variability or pre-existing difference between the subjects

·   How do we calculate the paired-samples t-test?

o   Use difference scores to calculate t

§  Numerator: compare mean difference score to zero

§  Denominator: Use variability in (and N of difference scores)

·   Definitions

o   Paired-samples t-test

§  A statistical test that compares the mean difference between two related samples

o   Repeated measures (or within-subjects) designs

§  Several measurements from the same participants

o   Matched samples design

§  The groups are naturally or explicitly connected or matched in specific pairs

o   Difference scores

§  The difference between two measurements or ratings from the same person or thing

The independent-samples t-test (Lecture, activities, & PsycLearn J)

·   When is the independent-samples t-test used?

o   When studying differences between two independent samples (1 between-subjects IV, 2 levels)

·   How do we estimate population variance based on two samples?

o   Adjusting for sample size by pooling the two sample variances and two sample sizes together

·   What is the logic of the calculations for the independent-samples t-test?

o   To compare the difference between the means of two independent groups, taking into account the variability within each group, to determine if the observed difference is statistically significant enough to conclude that the population means are likely different

·   How do we calculate the independent-samples t-test?

o   Taking the difference in the two sample means and dividing by either pooled or unpooled estimated standard error

·   Definitions

o   Independent-samples t-test

§  A statistical test that compares the difference between the means of two unrelated samples

o   Pooled variance

§  The weighted mean of the variance for both groups in an independent-sample t-test

Other

·   Make sure you are able to provide examples of & recognize studies analyzed with a particular type of z- or t-test.

·   Make sure you know how to use the z-table and t-table (they will be provided).