Lab #9 - Statistical Tests
Review:
- Correlation
- Used when interested in assessing the strength of association between two variables
- Used with continuous variables
- is the Greek letter rho, which is the population parameter tested in hypotheses (remember what parameters are from intro statistics?)
- r is the sample statistic that corresponds with
- correlation is statistically significant if the r value surpasses the critical value of r (use a statistical table or computer program)
- Example research hypothesis: Are higher levels of self-esteem associated with lower levels of depression (What is the null hypothesis? What direction correlation would be expected under the alternative/research hypothesis?)
- Regression
- Like correlation, used to assess the strength of association between two variables
- Two differences from correlation:
- Regression is used when primary interest is predicting scores, not just association between all scores
- Regression is used with one IV and one DV (e.g., conscientiousness predicting job performance); it is also used when there is more than one IV (e.g., ability, conscientiousness, and interest in the job predicting job performance), and in that case it is called multiple regression – your final project however only has one IV
- Used with continuous variables
- (beta) is population parameter tested in hypotheses
- b (slope of regression line) is the sample statistic corresponding with
- regression is statistically significant if t-statistic for b is greater than the critical value of t (use a statistical table or computer program)
- Example research hypothesis: Does higher self-esteem in middle childhood lead to lower levels of depression in adolescence? (notice this is different than correlation in that here we’re interested predicting scores)
- Independent samples (between-groups) t-test
- Used to determine mean differences in the dependent variable fortwodifferent groups
- Used with categorical or dichotomous variables
- Only one independent variable with only two levels/groups
- (mu) is population parameter tested in hypotheses
- (x-bar) is sample statistic corresponding with
- t-test is significant if t-statistic for is less than/greater than the critical values of t
- Example research hypothesis: Do women have higher levels of depression on average than do men (gender defines 2 independent groups, a continuous measure of depression is the DV)?
New:
- Analysis of Variance (ANOVA)
- Like t-test, used to determine dependent variable mean differences between groups/levels, but can use when there are more than two groups (which is the same as more than two levels of your IV)
- Remember, though, you’re still only using one IV, just there are more than two groups/levels (e.g., you might have the IV of political party, with the groups being Democrat, Republican, and Independent)
- Can use for your final project if you have just one IV with more than two groups (i.e., one-way ANOVA). ANOVA can also be used for more than one IV (i.e. two-way ANOVA, where say you have political party [3 groups] that may differ by gender [2 groups] for a 23 two-way ANOVA)
- Independent variable hastwo or more levels; if you only have one IV with two levels, though, use a t-test, even though ANOVA would give you the same results (and if you have more than one IV then you aren’t following the directions for the final project! )
- (mu) is population parameter tested in hypotheses
- (x-bar) is sample statisticcorresponding with
- ANOVA is significant if F-statistic is greater than the critical values of F
- Example research hypothesis: Do psychology graduate students tend to have higher IQs than medical students, physics graduate students, and English graduate students (what is the IV, what is the DV)?
- Repeated measures (within-groups) t-test or ANOVA
- Used to test mean differences in the DV for the same group measured at two or more times
- The t-test involves an independent variable with two levels; ANOVA involves independent variable(s) with more than two levels (e.g., use ANOVA when over a year, the same group of clients is exposed to each of 4 types of group counseling [the IV], and for each type of counseling, the clients’ symptoms [the DV] are measured).
- Population parameters and sample statistics are the same for both the between-group t-test and ANOVA.
- Example research hypothesis for repeated-measures t-test: Do people like the taste of Pepsi more than Coke (where the same people would taste both types of pop)?
- Example research hypothesis for repeated-measures ANOVA: Does exposure to death metal music leads to better cognitive performance than exposure to jazz, classical, or country music (where the same people would perform a cognitive task [DV] after listening to each type of music [IV])?
Research Designs and Statistical Tests
What type of control do you have over your independent variables?
Non-experimental designs
No control over independent variables
Experimental designs
Control over independent variables
Hallmarks: manipulation of independent variables and random assignment to groups/ levels
Quasi-experimental designs
Only partial control over independent variables.
Participants are assigned to groups/ levels by means other than random assignment on at least one of the independent variables.
-Person by treatment quasi-experiment
-Natural experiments (e.g. tornado damage vs. no tornado damage)
Does each group receive different treatments/conditions or same treatments/conditions?
Different conditions = Between-group design
Same conditions = Within-group (repeated measures) designs
- Pretest - Posttest designs
How many independent variables in your design?
One IV (only one IV for your final project):
t-test
One-way ANOVA (F-test)
Correlation
Regression
Two:
Two-way ANOVA
Multiple regression
Three:
Three-way ANOVA
Multiple regression
What type of independent variables in your design?
Continuous
Correlation
Regression
Categorical
t-test
ANOVA
Note that the DV will be continuous no matter which type of IVs you have
How many levels/groups do your independent variable(s) have?
Continuous variables, strictly speaking, have an infinite number of levels
With continuous IVs, you include the full range of scores across a group of individuals (you could consider each unique scores as a “level”)
Categorical variables generally have two or more levels/groups/conditions/treatments
2 levels = t-test
2 or more levels = ANOVA
Example Research Designs and How to test?
Example 1: Hypothesis - Higher levels of alcohol use tends to result in greater impairment in reaction time. Three groups of participants are each given alcohol mixed with orange juice. Each of the three groups gets a different amount of alcohol that corresponds to a different blood alcohol level (.01, .05, .10). The fourth group serves as a control group and only receives orange juice without alcohol. Each group is measured on a reaction time task.
1st question: What is the independent variable(s)?
2nd question: Do researchers have control over IV (manipulation and random assignment)? Full or partial control?
So which type of research design?
3rd question: Are groups given different treatments or same treatments?
So, between-group design or repeated measures design?
4th question: How many independent variables?
So, what kind of tests could be used?
5th: Are they continuous or categorical?
So, what kinds of tests could be used?
6th question: How many levels/groups in the independent variable(s)?
So, what test?
Example 2: Hypothesis - Depressed and non-depressed people have different explanations for negative life events only when in a negative mood. Depressed and non-depressed participants are randomly assigned to two conditions: positive mood inducing task or negative mood inducing task.
1st question: What is the independent variable(s)?
2nd question: Do researchers have control over IV (manipulation and random assignment)? Full or partial control?
So which type of research design?
3rd question: Are groups given different treatments or same treatments?
So, between-group design or repeated measures design?
4th question: How many independent variables?
So, what kind of tests could be used?
5th: Are they continuous or categorical?
So, what kinds of tests could be used?
6th question: How many levels/groups in the independent variable(s)?
So, what test?
Example 3: Hypothesis - Greater involvement with violent media leads to higher levels of aggression in adolescents. Adolescents report on both their involvement with violent media and their aggressive behavior; adolescents' parents also report on their children's aggressive behavior.
1st question: What is the independent variable(s)?
2nd question: Do researchers have control over IV (manipulation and random assignment)? Full or partial control?
So which type of research design?
3rd question: Are groups given different treatments or same treatments?
So, between-group design or repeated measures design?
4th question: How many independent variables?
So, what kind of tests could be used?
5th: Are they continuous or categorical?
So, what kinds of tests could be used?
6th question: How many levels/groups in the independent variable(s)?
So, what test?
Example 4: Men and women differ in their attitudes about capital punishment. Men and women are asked to complete surveys describing their attitudes about capital punishment.
1st question: What is the independent variable(s)?
2nd question: Do researchers have control over IV (manipulation and random assignment)? Full or partial control?
So which type of research design?
3rd question: Are groups given different treatments or same treatments?
So, between-group design or repeated measures design?
4th question: How many independent variables?
So, what kind of tests could be used?
5th: Are they continuous or categorical?
So, what kinds of tests could be used?
6th question: How many levels/groups in the independent variable(s)?
So, what test?
For Project - Methods Section (steps 5 - 9)
Make sure to review Project Guidelines
Step 5: Type of design - talked about that today
Step 6: Sampling plan - talked about this a couple of weeks ago
-Make sure you define your population (don't mix up with your sample)
-Describe IN DETAIL how you will sample your participants (how will you find them, recruit them, get them to participate, protect their rights, etc.)
Step 7: Measurement
-Finding measures
-From existing literature that you're using for intro
-From Tests in Print, etc.
-Make your own
-Reliability and validity information
-Must list no matter where measure comes from
-Should be good reliability and validity for you to use measure
-If not listed (or you're making your own), you must describe how you'll find reliability and validity
-e.g. test-retest reliability (measure people twice, correlate)
-e.g. expert judgment of items for validity
-Describe, again, IN DETAIL, how you will administer your measures. If manipulating your IV in experiment, describe IN DETAIL the manipulation.
Step 8: Statistical procedure - talked about that today
Homework for Lab #9
For each of the five research hypotheses described below, list (a) which type of research design is employed (non-experimental, experimental, or quasi-experimental), (b) what type of statistical test you would use to test it (independent (between-groups) t-test, between-groups ANOVA, repeated measures t-test, repeated measures ANOVA, regression, correlation), and (c) whether external or internal validity is most threatened (this is from lecture material not lab). Explain your answers to receive full credit!
Research hypotheses:
- People who are on a high-fish diet will perform better on memory tests than people on a low-fish diet.
- Children will show higher levels of aggression after playing a violent video game. 7-year olds will be interviewed and measured on aggression when they first come into the study; they will be measured again immediately after playing 2 hours of a violent video game; and they will be measured one last time 3 days after the game was played.
- The degree to which someone believes in God relates to his/her level of risk-taking. Specifically, the more someone believes in God, the more willing he/she will be willing to take risks in life.
- People who are relaxed will have a better memory for the events of a crime than people in a stressed state or a control group. The first group goes through a progressive relaxation session and is then presented with a short (10-minute) video of a crime that was recorded on a security camera at a convenience store (called Fredway). The second group goes through a stress-inducing session – listening to loud music in a room with a strobe light – and then is presented with the same video. The control group does not go through any session; they are only presented with the video. After 2 hours, all groups are given list of events and have to answer true/false which ones occurred.
- Children will tend to perform slower (more carefully) on a multiplication task when they are competing with another person to get questions right vs. when they are by themselves and are told to do as many as they can under timed conditions. Children will be randomly assigned to the group vs. timed conditions.