– a “process” or a way of working with those numbers to address research questions

-researchers gather data (numerical), organizes it, and then analyzes it using various statistics tests to make inferences to answer the research questions

-based on statistical framework in order to make decisions in a systematic, objective manner

-generally involves making educated guesses or inferences from samples to a population

-when inferring from a smaller group to a larger one, it is essential that the smaller group represents the larger group, and this why random sampling is a critical part of the process

-more often than not, the degree of confidence is set at 95% or 99%

-usually the researchers tests the null hypothesis of “no difference” (if statistical significance is found, then the investigator rejects the null hypothesis

-a directional hypothesis, developed when there is adequate prior information to take such a prediction, can be used and tested if deemed appropriate (obtaining statistical significance is more likely when a directional hypothesis is used)

researchers develop a hypothesis or statement about the outcome of the investigation

-hypotheses can be stated in several ways (null, alternative, directional)

2) state the level of significance

3) compute the statistic

4)determine the critical region (1 tail or 2 tails)

5)reject the null hypothesis if the test statistic falls in the critical region. do not reject if it falls in the acceptance region

6) state appropriate conclusion

-many research efforts in health science establish the level of significance at the 5% alpha level, although it may be set at the .025, .01 or .001 levels

-rejecting the null hypothesis at the .05 level suggests that there is less than a 5% probability that the differences are caused by error or chance

-corresponds with the level of probability or significance

-the 5% area of rejection is split between the upper and lower tails of the curve since the null hypothesis is nondirectional

-the 5% area of rejection is at either the upper end or lower end of the curve

-the alpha level of significance determines the probability of a type ___ error

-as alpha level of significance increases, the possibility of a type 1 error is reduced, but the chance of a type 2 error (beta) increases

-typically, type 1 error leads to unwarranted changes, whereas type 2 errors maintain the status quo when a change should occur

-after the experimental group has been exposed to the treatment, the researchers may wish to compare the experimental to the control group.

-the mean is likely the most satisfactory measure for characterizing a group.

-a t-test is used to determine the probability that the difference between the means is a real difference rather than a chance difference.

-when the samples are greater than 30 subjects, the t critical values are expressed as z scores

(therefore the obtained t-value from the formula is compared with the z-distribution for acceptance or rejection of the null hypothesis.)

-When the samples are fewer than 30 in number, a t-table is used rather than the normal probability table (this is because the distribution curve is small samples are different from the normal curve)

The subjects may be matched on one or more characteristics, or the same subjects may be in a pretest-posttest experiment.

–>in such cases, the two groups are no longer independent, so a special t-test for dependent or correlated means is required.

–>the measure to be analyzed is the difference between the paired scores.

-if 2+ groups are involved, one of the most powerful methods for comparing means is analysis of variance (ANOVA).

-if there is only one independent variable in the study the ANOVA is called a one-way ANOVA.

-in ANOVA, as in the t-test, a ratio of observed differences/error is used to test hypotheses.

(the ratio, called the F-ratio, uses the variance of group means as a measure of observed differences among groups)

-represents the sampling error in the distribution

-shows the influence of the experimental variable or treatment

-if the F-ratio is substantially greater than 1, it would appear that the difference is likely the result of the treatment.

-to determine whether the F-ratio is great enough to reject the null hypothesis (at the pre-determined level of significance), consult an F-table, which contains the critical values necessary for testing.

-the analysis of variance is the first step in the analysis of such designs.

-if a significant F-ratio is obtained, it is only known that somewhere in the data something other than chance is operating.

-differ somewhat in their ability to produce significant results

Examples of special t-tests:

-Duncan’s multiple range tetst

-Tests by Newman-Keuls, Turkey, Bonferroni, and Scheffe

-researcher mus employ a special form of the t-test to isolate the presence, nature, and extent of influencing variable

-researchers must be able to justify the post hoc test used

-ANCOVA can also be of value when comparison groups can only be matched on the principal variable and not on others.

-determine the contribution of one or more independent variables on the dependent variable (outcome).

-can also be used to predict the value of one variable over that of other variables.

-it is the simplest form of prediction since only one predictor variable is used

-used in several ways, and it is recommended that texts dealing with this statistical technique be consulted.

–>population scores are NORMALLY DISTRIBUTED about the mean

–>population variances of the groups are approximately equal

When deviations from these assumption are in the data, parametric statistics should not be used

–>nonparametric statistical tool should be selected

–>these techniques don’t make any assumptions about the population variance or shape of the data

-they are very suitable for health surveys and experiments in which outcomes are difficult to quantify

-they offer ease of computation

-less specific

-fail to deal with all the special characteristics of a distribution

-The Mann-Whitney U-Test

-The Sign Test

-The Median Test

-The Wilcoxon Matched-Pairs Signed Rank Test

-The Kruskal-Wallis Test

-The Kendall Coefficient of Concordance

Nine steps in conducting a good systematic review including meta-analysis.

-cost of conducting the study

-criteria being used for including primary sources are difficult to agree upon

-incomplete data are sometimes used because they are the only data available.

-providing a systematic overview of findings in a particular area of study

-determining larger research questions

-enabling an alternative method when other methods are inappropriate

-being able to conduct methodological assessments of research designs

A result from a factorial design, in which the difference in the levels of one independent variable changes, depending on the level of the other independent variable; a difference in differences

A study in which there are two or more independent variables, or factors.

In the most common factorial design, researchers cross the two independent variables; that is, they study each possible combination of the independent variables.

The process of using a factorial design to test limits is sometimes called testing for moderators. (moderator: variable that changes the relationship between two variables)

Ex: older people driving while using cell phones, driving while not using cell phones, and younger people driving while using cell phones, or driving while not using cell phones

A variable such as age, gender, or ethnicity whose levels are selected (i.e., measured), not manipulated.

main effect = overall effect : the overall effect of one independent variable at a time.

may or may not have statistical significance

2. Factorial designs can test theories; can test generalizability of a causal variable and also test theories.

Each participant does both the manipulated and the control conditions of the study.

interaction

main effect

overall effect

mediation

age

sex

years of education

treatment group

the main effect of the first independent variable

the interaction

the main effect of the second independent variable

the overall effect

within-groups factorial design

mixed factorial design

independent-groups factorial design

nested factorial design

type of commercial shown

amount of alcohol consumed during the movie

young adults who consume small amounts of alcohol each week

the movie shown

type of commercial shown

amount of alcohol consumed by the young adult during the week

amount of alcohol consumed during the movie

the movie shown

to increase construct validity and to test theories

to increase construct validity and to increase internal validity

to test the limits of an effect and to test theories

to use fewer participants and to test the limits of an effect

factorial

repeated measures

concurrent measures

pretest-posttest

mediating

moderating

confounding third

main effect

Moderating variables

Factorial designs

Interaction effects

Marginal means

two main effects and a two-way interaction??

three main effects and three-way interaction

three main effects, three two-way interactions, and a three-way interaction

three main effects, three two-way interactions, and three three-way interactions

20

40

60

120

2 independent variables, 4 cells

2 independent variables, 9 cells

3 independent variables, 9 cells

3 independent variables, 24 cells

correlation

main effect

interaction effect

significant

the phrase “it depends”

reference to a peer-reviewed journal

the use of a participant variable as well as another independent variable

phrasing that suggests that there was a difference in the differences

1

3??

8??

16

The alcohol commercial increased the alcohol consumption of all viewers.

The effect of the alcohol commercial on alcohol consumption depended on whether the viewer was usually a heavy drinker or a light drinker.

The alcohol commercial had no effect on the consumption of alcohol.

The effect of the alcohol commercial on alcohol consumption was unpredictable.

tastiness and expensiveness

price

picture

consumer

independent-groups factorial design

within-groups factorial design

mixed factorial design

concurrent measures design

2 x 2

1 x 2

2 x 2 x 2

2 x 4

two parallel horizontal lines

two parallel diagonal lines

two parallel vertical lines

two crossed lines

1

2

3

6

the number of pictures accurately identified

race of the personality in the picture

personality of the person in the picture

race of the participant

a main effect

a two-way interaction between race and personality

a two-way interaction between Caucasian and personality

a three-way interaction between race, personality, and accuracy

three main effects and two interactions

two main effects and two interactions

three main effects and one interaction

two main effects and one interaction

– difference in differences = the effect of one independent variable on the dependent variable depends on on the level of the other independent variable

– one line flat, one line increase or decrease but never cross

i.e. researcher studies two school districts and then three schools within each district (district is first IV and three schools are second, nested, IV)

i.e. age, sex, ethnicity, and culture

– not truly independent variables

-would cell phone use while driving only affect one age group? or have same effect on people of different ages?

-function as form of external validity: testing whether effect generalizes (when IV effects groups in the same way. suggests effect generalizes to all)

-Interactions show moderators

– Test Theories

-the effect of using a cell phone did not differ with age = cell phone use did not interact with age.

-in factorial language moderator is an independent variable that changes the relationship between another independent variable and a dependent variable. (results in an interaction)

i.e. driver age did not moderate impact of cell phone use on brake time

– not necessarily most important

-simple difference

– may or may not be statistically significant (if not- no effect)

-interaction is almost always more important

– in a 2×2 there are four independent groups

– in a 2×2 there is only one group of participants who participate in all four combinations

– i.e. old and young group, each group drove with and without cellphone condition

-strayer and and drews

^ level of each dependent variable

– with each additionial variable need to test main effect ( 2x2x2) need to test for three main effects

-two main effects and one interaction

There are two independent variables, so there are two main effects and one interaction possible, even though one variable has three levels.

How many cells was each golfer in?

-6

If this was just a 2 × 2 within-groups design, it would need just 20 participants. Adding the third between groups factor makes 60 necessary: 20 for each level.

-This means that in looking at the tastiness/expensiveness ratings for self, there is a larger difference between the attractive and unattractive ratings than there is in those ratings for classmate.

-This means that in looking at the tastiness/expensiveness ratings for self, there is a smaller difference between the inexpensive and expensive ratings than there is in those ratings for classmate.

-The marginal means are the same for both factors and there are differences in the differences in each column.

-The weekly alcohol consumption of the participant was selected, not manipulated.

price

picture

all of them are manipulated <<<

-This wording suggests that the dependent variable was changed by the anxiety manipulation in the technique condition, but not in the other conditions.

-Increasing the Number of Levels of an Independent Variable—The marginal means differ for both factors and there are differences in the differences in each column.

-Marginal means are used to inspect the main effects, and in the case of a not significant main effect of anxiety, they are very close to each other.