week 11-statistical tests

Question 1

Comparing two group means in an RCT

Assumptions

Answer 1

• assume groups at pretest are baseline
• difference between groups at posttest is due to treatment
• unlikely to be result of chance

Question 2

Comparing two group means in an RCT: parametric assumptions

Answer 2

• groups have normal distributions
• groups have variances
• interval/ratio data is used
• compare the difference between groups with a t-test

Question 3

Statistical error

Answer 3

• all sources of variability within a data set that cannot be explained by IV (not necessarily mistake)
• applies to the random differences that are not explained by treatment
• source of error is variance - all subjects in groups do not respond the same

Question 4

T distribution

Answer 4

• based on properties of normal curve (95% within 2 SD from mean)
• determine z-score of area of curve above and below that value and probability of obtaining score
• significance of difference between the two groups judged by ratio
• t=difference between means/variability within groups
• H0 is true if error variance increased and t ratio decreased
• H0 is false if error variance decreases and t-ratio is increased

Question 5

Independent Unpaired t-test

Answer 5

• compare means from 2 independent groups (between subjects design)
• each group composed of difference set of subjects
• t=(X1-X2)/(Sx1-X2) = difference between independent groups/pooled variability within groups
• compare calculated t-value with critical value
• probability that calculated t-value will be larger than critical value is 5% or less
• t-value larger than critical value is considered significant and reject the h0

Question 6

Two-tailed test (nondirection HA)

Answer 6

• non directional hypothesis (meaning that they are not saying one group will be more/less they are saying there will be a difference.)
• two groups

Question 7

paired t-test

Answer 7

• subjects serve as own control (within subject design)
• each measurement has a matched value for each subject
• determin if these are significantly different from each other
• t=mean of difference scores/standard error of difference scores

Question 8

use of multiple t-tests

Answer 8

• compare two means
• if > 2 means should not compare using multiple t-tests
• making more comparisons means you are more likely to commit type 1 error
• 5% chance of type 1 error with each test
• cummulative error of multiple test >5%

Question 9

ANOVA basics

Answer 9

• purpose: compare 3+ groups
• like t-test based on comparison of distance between group means and error of variance of each group
• parametric assumptions:
  1. normal distribtuion
  2. homogeneity of variance
  3. interval/ratio data

Question 10

One-way NOVA

Answer 10

• one IV (3+ levels)
• h0: uA=uB=uC…
• HA: there will be a difference between at least two of the groups
• Calculates f-statistic
• conclusions: reject H0 if there is a significant different but you do not know where it is

Question 11

Multiple comparision test: one-way ANOVA

Answer 11

• if a significant difference is found you must carry out a post hoc multiple comparison test to locate differences

Question 12

two-way ANOVA

Answer 12

• 2 IV (factor a and factor b)
• null hypothesis for each main effect of the factors
• if significant difference is found a mulitple comparisions for 2-way ANOVA test should be conducted

Question 13

Chi-Square: nonparametric test

Answer 13

• not based on assumptions about population distribution
• use rank or frequency information to draw conclusions about difference between population
• use with categorical variables (nominal data)

Question 14

Chi-square assumptions

Answer 14

• frequencies represent individual counts
• categories are exhaustive and mutally exclusive

Question 15

chi-squared equation

Answer 15

• summation of (O-E)^2/E
• statistic based on differences between observed frequencies and frequencies that would be expected if null hypothesis were true

Question 16

two-groups parametric tests

Answer 16

• independent t-test: between subject design
• paried t-test: within subjects design

Question 17

3 + groups parametric design

Answer 17

• ANOVA: 1 IV
• Multifactorial: ANOVA (2-way, 3-way etc) with 2+ IV
• if significance is found then multiple comparisons to locate difference

Question 18

Categorical data: nonparametric

Answer 18

• chi-squared: compares observed frequency with expected frequency

Question 19

correlation research

Answer 19

• analysis of association between variables
• nonexperimental, no IV, observe existing phenomena
• interval/ratio data

Question 20

Correlation coefficient

Answer 20

• test statistic: r - describes strength and direction of relationship between 2 varibles
• values range from -1 to 1

Question 21

positive value for correlation coefficient

Answer 21

• positive correlation
• direct relationship

Question 22

negative value for correlation coefficient

Answer 22

• negative correlation
• indirect relationship

Question 23

assumptions for correlation

Answer 23

• subjects scores represent normally distributed population
• each subject contributes a score for X and Y
• X and Y are independent measures
• X values are observed not controlled
• relationship between X and Y is linear

Question 24

Hypothesis testing in correlation

Answer 24

• significant correlation is unlikely to have occured by chance
• H0: population correlation = 0
• HA: population correlation doesnot = 0

Question 25

Interpreting correlation coefficients: strength of relationship

Answer 25

- .00-.25=little correlation - 0.26-0.49 = low correlation - 0.5-0.69 = moderate correlation - 0.7-0.89 = high correlation - 0.9-1.00 very high correlation OR - 0-.25 = low - 0.26-.5 = fair - 0.51-.75= moderate - 0.76-1 = high | `

Question 26

Interpreting correlation coefficients: coefficient of determination

Answer 26

- square of correlation coefficient r - percentage of variance shared by the 2 variables - if r=0.76, r2=0.58 that means 58% of variability in one variable can be accounted for be the other variable

Question 27

Statistical significance

Answer 27

- probability that correlation coefficient would have occurred by chance if there was no correlation between variables - even weak correlations can have statistical significance