Hth 320 chapter 10

example of within subjects design

studying effect of exercise on memory, could have participants take a memory test after aerobic exercise and then again after anaerobic exercise

There are three measures of effect size for the related-samples t test

-Cohen's d -Eta-squared -Omega-squared

Why can Selecting related samples can be more practical

-May provide a better way to test your hypotheses -it may be more practical to observe behavior of the same participants before and after some treatment (repeated measures) or to compare how well participants of a similar ability master some task (matched samples)

Two types of Repeated Measures designs

-Pre-post design -Within-subjects design

why does Selecting related samples minimizes standard error

Computing difference scores prior to computing the test statistic eliminates the between-persons source of error, which reduces the estimate of standard error

the test statistic

MD : sample mean difference; μD: pop. mean difference -The larger the value, the less likely a sample mean difference could occur if the null hypothesis were true

point estimate for a related-samples t test

Md

IMPORTANT

Population mean = Point estimate Interval estimate

Follow three steps to estimate the value of a population mean using a point estimate and interval estimate

Step 1: Compute the sample mean and standard error Step 2: Choose the level of confidence and find the critical values at that level of confidence Step 3: Compute the estimation formula to find the confidence limits

Related or dependent sample

participants in each group or sample are related

cohnes D

-Most common measure of effect size used for the t test -d measures the number of SDs that mean difference scores shifted above or below the population mean difference stated in the null hypothesis

types of t tests

-independent sample t test -one sample t test -related sample t test

interval estimate for a related-samples t test is

t(SMd)

Related Samples Summary

-Repeated measures can be selected by observing participants before and after a treatment (pre-post design) or across treatments (within-subjects design). -Matched pairs can be selected through experimental manipulation or natural occurrence.

repeated measures design

-research design in which the same participants are observed in each sample. -the same people are being assessed multiple times - This is the most common related samples design.

difference score

-score or value obtained by subtracting two scores. In a related samples t test, this is obtained prior to computing the test statistic -We subtract pairs of scores first, then compute the test statistic, which eliminates the source of error associated with observing different participants in each group or treatment

Pre-post design

-type of repeated measures design in which researchers measure a dependent variable for participants before (pre) and following (post) some treatment -Limited to observing participants at two times -participants will either be in a comparison group or a control group -sometimes there will not be a comparison group and all partiapntsw will get the same intervention

why does Selecting related samples increases power

Reducing the estimate for standard error will increase the value of the test statistic

estimated standard error for difference scores

is placed in the denominator. The standard error for a distribution of mean difference scores is computed

a researcher asks a sample of brothers and sisters to rate how positive their family environment was during childhood. in this study, the differences in ratings between each brother and sister pair were compared. the type of design described here is called

matched pairs -naturally occurring design

a researcher compares the difference in the amount of texting by students in class during the first week and last week of classes. the type of design describes is

repeated measures design -within subject design

normality

we assume data in the population of differences scores are normally distributed

independence within groups

we assume that difference scores were obtained from different individuals within each group or treatment

example of matching through natural occurence

you could match participants based on genetics (e.g., biological twins)

example of pre post design

you could measure athletic performance in a sample of athletes before and after a training camp

example of matching through experimental manipulation

you could measure intelligence then match the two participants scoring the highest, the two scoring the next highest, and so on

Advantages for Selecting Related Samples

-Selecting related samples can be more practical -Selecting related samples minimizes standard error -Selecting related samples increases power

how are participants related in a related t test

-They are observed in more than one group (repeated measures design) -They are matched, experimentally or naturally, based on the common characteristics or traits that they share (matched-pairs design)

APA in Focus: Reporting the t Statistic and Effect Size for Related Samples

-To summarize a related samples t test, report the test statistic, df, and p value -Summarize means and standard error or SDs measured in the study in a figure or table or in the main text -When reporting results, it is not necessary to identify the type of t test computed -This is typically reported in the data analysis section

estimation formulas

-You can use estimation as an alternative to each t test -two related samples is to identify the confidence limits within which the mean difference between two related populations is likely to be contained

related sample t test

-a statistical procedure used to test hypotheses concerning two related samples selected from populations in which the variance in one or both populations is unknown -Comparing mean difference between pairs of scores in population to those observed in a sample

There are two assumptions you make to compute the related-samples t test

-degrees of freedom -normality -independence within groups

a teacher compares final exam scores in her health class to final exam scores in another comparable teacher class. what type of t test is appropriate for analyzing differences

-independent sample t test -two different samples -no population samples

a researcher conducts a study comparing the lung cancer rate in a small community to the known lung cancer rate in the US. What type of t test is appropriate for analyzing differenes?

-one sample t test -usually with a big population -a single sample compared to a population sample

matched pair design

-research design in which participants are selected and then matched experimentally or naturally, based on the common characteristics or traits they share -Limited to observing two groups where pairs of participants matched -Different, yet matched, participants are observed in each treatment

Matching through experimental manipulation

-typical for experiments in which the researcher manipulates the traits or characteristics used to match the participants -Must measure some trait or characteristic before matching

Within-subjects design

type of repeated measures design where researchers observe the same participants across many treatments but not necessarily before and after a treatment

Matching through natural occurrence

typical for quasi-experiments in which participants are matched based on their preexisting traits or characteristics