Research Chapter 21 Test 2

Front 1

What is the magic rule about DV and IV for test of differences?

Back 1

Dv: ratio, IV: nominal or ordinal

Front 2

Parametric tests:

Back 2

based on specific assumptions about the distribution of populations; inferential statistics

Front 3

Use sample statistics (mean, standard deviation, variance)- dealing with parametric tests

Back 3

to estimate differences between population parameters.
• Two classes: T tests and analyses of variance (ANOVAs)
• More powerful than nonparametric tests(more robust)
• Cannot always be used because the assumptions on which they are based are more stringent than the assumptions for nonparametric tests

Front 4

• Two assumptions that are accepted

Back 4

random selection and homogeneity of variance. Third assumption: controversial and relates to the measurement level of the data

Front 5

Random selection:

Back 5

participants are randomly selected from normally distributed populations.
• Don’t have to have randomly selected participants IF the variables used in the analysis are relatively normally distributed in the population you are studying (scatterplots, stem and leaf plots)
• How do you deal with non normal data-
1)can convert or transform the data mathematically: squaring, taking square root, or calculating a logarithm of raw data (not going there!) or 2) use nonparametric tests

Front 6

Homogeneity of variance:

Back 6

population variances of the groups being tests are equal (homogeneous)
• Tested statistically
• If variances between the groups differ significantly, use nonparametric tests
• Sample sizes are the same, differences in variances of the groups become less of a concern
• Researchers aim to have equal sample sizes

Front 7

Level of measurement:

Back 7

Parametric tests require data from which means and variances can be calculated (interval and ratio data only)
Problem is with ordinal data
Validity of using only interval/ratio data for parametric tests
o As long as data themselves meet the parametric assumptions, regardless of origin of the numbers (read ordinal data), then parametric tests can be conducted BUT you have to base your conclusions based on the use of ordinal data in the clinic
• It is reasonable to conduct parametric tests with ordinal data as long as interpretation of the tests accounts for the nature of the ordinal scale (figure 18-1; p. 231)

Front 8

Independent:

Back 8

values in one set tell nothing about values in another set .Two or more groups consist of different, unrelated individuals, the observations made about the samples are independent.
• Ex: 3 week ROM scores for patients in Clinics 1-3 are independent of one another

Front 9

Dependent:

Back 9

sets of numbers consist of repeated measures on the same individuals. (Husband/wife, other relatives, matched pairs) 3 week, 6 week, and 6 month ROM scores for patients across the three clinics are dependent measures.

Front 10

Nonparametric tests:

Back 10

not based on specific assumptions about the distribution of populations. (much looser)
• Use rank or frequency information to draw conclusions about differences between populations (nominal and ranked ordinal data). Interval and ratio data can be converted into ranks or grouped into categories.

Front 11

Independent t test:

Back 11

Parametric test of differences between two independent sample means
• Test statistic: ratio of the differences between the groups (numerator) to the differences within the groups (denominator)
• Ratio of differences is explained by the independent variable
• Differences within the groups is unexplained- do not know what leads to individual difference between subjects
• When the variability explained by the independent variable is sufficiently large compared with the unexplained variability, the test statistic is large and a statistically significant difference is identified.

Front 12

Mann-Whitney test or Wilcoxon rank sum test:

Back 12

Nonparametric alternative to the independent t test
• Use this if assumptions for the independent t test are violated

Front 13

Mann-Whitney test or Wilcoxon rank sum test:

Back 13

• Hypotheses need to be stated in more general terms than the hypotheses for parametric tests:
o Ho: the populations form which Clinic 1 and clinic 2 samples are drawn are identical
o H1: one population tents to produce larger observations than the other population
• Mann-Whitney: rank the scores from the two groups, regardless of original group membership. When a number occurs more than once, its ranking is the mean of the multiple ranks it occupies. Ex: two 67s are the 11th and 12th scores so each receives a rank of 11.5. Next rank is 13.
• Alternative form of Mann-Whitney: U statistic converted into a z score
o Done by a computer

Front 14

F statistic:

Back 14

need to know the individual group means as well as the grand mean
F= MSB/MSW

Front 15

Grand mean:

Back 15

mean of all the scores across the groups

Front 16

Total sum of squares (SST):

Back 16

the sum of the squared deviations of each individual score from the grand mean. (total variability)

Front 17

Within group sum of squares (SSW):

Back 17

the sum of the squared deviations of the individual scores from the group mean. (Group variability)

Front 18

Between group sum of squares (SSB):

Back 18

the sum of the squared deviations of the group means from the grand mean. (Between groups variability)

Front 19

SST= equation...

Back 19

SSB+ SSW

Front 20

Mean square between groups

Back 20

(MSB)
• MSB= SSB/ (groups -1)

Front 21

o Mean square within each group

Back 21

MSW)
• MSW= SSW/ (N-groups)

Front 22

What does a large F value mean?

Back 22

indicate that difference between the groups are large compared with the differences within groups.

Front 23

What does a small F value mean?

Back 23

indicated that the differences between groups are small compared with the differences wihin groups

Front 24

• Multiple comparison tests:

Back 24

similar to t tests but with a correction to prevent inflation of the alpha level
o EX: Bonferroni test

Front 25

Kruskal-Wallis test

Back 25

o Nonparametric equivalent of the one way ANOVA
• Use if the assumptions of the parametric test are not met
o Ho: the three samples come from populations that are identical
o H1: at least one of the populations tends to produce larger observations than another population

Front 26

How do you conduct a Kruskal-Wallis test?

Back 26

• Rank scores regardless of group membership
• Ranks are summed and plugged into a formula to generate a Kruskal wallis (KW) statistic.
• If this is lower than the alpha level- there is a significant difference among the groups
• When there is a difference, use Mann Whitney test with a bonferroni adjustment of alpha as the multiple comparision procedure

Front 27

How to calculate paired t test?

Back 27

• Determine the difference between each pair of measurements
• Determine mean difference and standard deviation of the differences and the mean is compared with a mean difference of zero.
• Calculate the t statistic for paired samples by dividing the mean difference by the standard error of the mean differences
• If t statistic is……

Front 28

Wilcoxon Signed Rank test:

Back 28

nonparamentric version of the Paired t test
o Ho: the difference between the population medians is equal to zero
o H1: the difference between the population medians is not equal to zero

Front 29

To conduct Wilcoxon Signed Rank test:

Back 29

• Calculate the difference between each pair of numbers
• Rank the nonzero differences according to absolute value
• Separate them into ranks associated with positive and negative differences
• If there is no difference from one time to the next, the sum of the positive ranks should be approximately equal to the sum of the negative
• Ranked information transformed into z score (by computer)
• Since this is less than alpha of.05, there is a significant difference btween the scores
• To determine the clinical importance of the difference, we look at the median of the difference btween the two samples.

Front 30

Repeated Measures ANOVA:

Back 30

extension of a paired t test to more than 2 dependent samples

Front 31

Three different approaches:

Back 31

o Multivariate
o Univariate
o Adjusted univariate

Front 32

o Univariate

Back 32

• First partitions the variability in the data set into btween subjects and within subject categories
• The within subject variability is then subdivided into between treatments and error components

Front 33

• Two F ratios can be generated:

Back 33

• 1) ratio of btween subjects to within subject varability
o Sometimes reported but not relevant to the research question
• 2) ratio of btween treatments to residual variability

Front 34

• Repeated measures ANOVA

Back 34

mathematically eliminates between subjects variability to focus the analysis on within subject variability

Front 35

Freidman’s ANOVA

Back 35

Nonparametric equivalent of the repeated measures ANOVA
Calculation is based on rankings of the repeated measures for each participant
Computer computes either a Friedmans F or Friedmans’ chi square
Ex:p 292

Front 36

If you have done an one way ANOVA---

Back 36

you would do an independent t test

Front 37

If you have done a repeated measure ANOVA---

Back 37

you would do a paired T test