Week 8 - Inferential Stat Methods

Question 1

what is inferential stats?

Answer 1

• based on the laws of probability
• requires a random sample for best representativeness (gold standard is probability sampling, but is often widely violated, i.e. need something like NHANES or large funds)
• cause/effect
• compares groups
• determines relationships among variables, etc.

Question 2

t/f - Even if it’s a random sample, it’s rarely identical to the real population

Answer 2

true

Question 3

what is sampling error?

Answer 3

tendency for statistics to fluctuate from one sample to another; the challenge is how to decide whether estimates are good population parameters?

Question 4

what is sampling distribution of the mean?

Answer 4

a theoretical distribution of a test statistic (i.e., mean) from an infinite number of samples as data points.

Question 5

what is a standard error of the mean (SEM)?

Answer 5

standard deviation (SD) of a sampling distribution of the mean (i.e. estimated from the sample’s SD and the sample size)

Question 6

what happens in a normally distributed population…

Answer 6

• 68 out of 100 of any randomly drawn sample means lies between +1 SD and -1 SD of the population mean.
• Larger sample size ► we can increase the accuracy of our mean estimate

Question 7

what are the two forms of statistical inference?

Answer 7

• estimation of parameters (not as common in nursing research)
• statistical hypothesis testing

Question 8

what is an example of estimation of parameters (trying to estimate for the entire population)?

Answer 8

• NCLEX pass rate for all individuals taking exam within a set time window
• States w/laws requiring employers to offer paid sick leave for FT and PT staff nurses: Gaps in the Emergency Paid Sick Leave Law for Health Care Workers | KFF

Question 9

what is an example of hypothesis testing (for a particular sample or group)?

Answer 9

• Impact of investigational drug compared to placebo on BP

- Impact of nursing intervention to prevent burnout and turnover

Question 10

what are the two forms of parameter estimation?

Answer 10

• point estimation

- interval estimation

Question 11

what is point estimate (as a form of parameter estimation)?

Answer 11

calculating a single statistic (i.e. sample mean) to estimate the population parameter (i.e. population mean)

Question 12

what is interval estimation (as a form of parameter estimation)?

Answer 12

calculating a range of values the parameter (i.e. population mean) has a specified probability of being located

Question 13

what is the confidence interval?

Answer 13

95-99%

Question 14

what is confidence limits (CL)?

Answer 14

the range of values for the population and the probability of being right with a certain degree of confidence (i.e. 95% or 99%).

Question 15

what are things to keep in mind about binomial distribution?

Answer 15

• CIs are rarely symmetric like this picture
• Width of CIs depends on sample size and proportion values
• CIs for proportion values never extend <0 to >1, but can be constructed around proportions of 0 or 1

Question 16

what are the typical CI proportions constructed on a binomial distribution?

Answer 16

ARR = absolute risk reduction
RRR= relative risk reduction
OR = odds ratio
NNT = number needed to treat

Question 17

what is hypothesis testing?

Answer 17

-Objective criteria for deciding if hypotheses are supported by data
-Based on rules of negative inference: Research hypotheses are supported if null hypotheses (H0) can be rejected
-Researchers want to accept or reject H0
H0 = there are no mean differences between groups
HA= there are mean differences between groups
-Uses statistical decision-making to either reject or accept H0

Question 18

what is the simplest way to decrease type ll error?

Answer 18

increase the sample size

Question 19

t/f - making decisions to decrease type l error decreases the risk of type ll error

Answer 19

false - making decisions to decrease type l error increases the risk of type ll error

Question 20

what is type l error?

Answer 20

• the H0 is rejected when it should not be (false positive)

- Risk of Type I Error is controlled by significance (α or p-value) of 0.05 or 0.01

Question 21

what is type ll error?

Answer 21

• accepting the H0 when it should be rejected (false negative)
• Risk of Type II Error is controlled by setting power (1-β) at 80%

Question 22

t/f - There is no “almost” significant at p=0.06

Answer 22

true

Question 23

researchers compute a test statistic with their data for what reason

Answer 23

determine whether the statistic falls beyond the critical region in the relevant theoretical distribution

Question 24

what is bivariate tests?

Answer 24

analysis of 2 variables to assess the empirical relationship between them

Question 25

what is a non-significant result?

Answer 25

means that the relationship is from chance fluctuations (accept H0)

Question 26

what is a significant result?

Answer 26

means that the H0 is very improbable and thus statistically significant (reject H0 and accept Ha)

Question 27

what is normal theoretical probability distributions?

Answer 27

Each test statistic has its own mathematic proportions for calculating critical value-limit scores falling within normal theoretical probability distributions.

Question 28

what are examples of normal theoretical probability distributions?

Answer 28

- t Distribution for t-tests - F Distribution for ANOVA tests - χ2 Distribution - r Distribution

Question 29

what is a two-tailed test?

Answer 29

Hypothesis testing in which both ends of the sampling distribution are used to define the region of “improbable” values.

Question 30

what are the pros of two-tailed tests?

Answer 30

you do not need to know in advance the alternative hypothesis

Question 31

what are the cons of two-tailed tests?

Answer 31

you may not be able to detect small differences

Question 32

what is a one-tailed test?

Answer 32

Critical region of improbable values is entirely in 1 tail of the distribution—corresponding to the direction of the hypothesis set by the researcher

Question 33

what is a pro of one-tailed test?

Answer 33

offers you more power to detect small differences

Question 34

what are the cons of one-tailed test?

Answer 34

must guess the right direction in advance; even if a large effect, if it is in the wrong direction, it must be written off due to chance (thus a less conservative approach)

Question 35

what does the sampling distribution look like for two-tailed tests?

Answer 35

5% of the sampling distribution is equally split b/t 2 tails: 2.5% on each side

Question 36

what is the sampling distribution of a one-tailed test?

Answer 36

5% of the sampling distribution is on 1 side

Question 37

what are parametric stats?

Answer 37

- Involves the estimation of a parameter - Requires measurements on an interval/ratio scale - Involves several assumptions (i.e. variable w/normal distribution) - pearson's r - preferable

Question 38

what are non-parametric stats?

Answer 38

- Does not estimate parameters, uses a rank ordering procedure - Uses variables/data on a nominal or ordinal scale - Do not involve a distribution (distribution-free statistics) - Has less restrictive assumptions about the shape of the variables’ distribution than parametric tests (i.e. multiple peaks, outliers, abnormal distribution) - spearman's rho - small sample size

Question 39

what is a bonferroni correction?

Answer 39

- designate a more conservative α threshold = p-value/# of total tests; 0.05/6 = 0.0083 - reduces type l error

Question 40

what falls under the category of parametric (interval or ratio)?

Answer 40

- Student’s Independent t-test - Paired (Dependent) t-test - ANOVA (1,2 way ANOVA), (DV for 3 groups on 1 or 2 IV) - Repeated Measure ANOVA (3 Groups over different time pts) - Pearson-Product Moment (pearson’s r)

Question 41

what falls under non-parametric (highly skewed or non-interval, non-ratio) tests?

Answer 41

- Mann-Whitney U test - Wilcoxon signed ranks test - Kruskal Wallis - Friedman Test - Spearman Rank Correlation (phi coefficient)

Question 42

what is a chi-square test?

Answer 42

- A statistical test used to determine if group differences in a cross-tabs (or proportions of categories in 2 group variables) differ from one another - Computed by summarizing differences b/t observed vs expected frequencies for each cell - Assumes a random sample, independence, and mutually exclusive groups

Question 43

what is pearson's r (correlation)?

Answer 43

- a correlation coefficient; designates the magnitude of relationship (strength and direction) between two variables measured on at least an interval scale; can be used between group and within group situations - Interpreting r Values: -1 (Negative correlation) to 1 (Positive Correlation); 0 = No correlation - Both descriptive and inferential

Question 44

what is descriptive correlation?

Answer 44

summarizes the magnitude of relationship b/t 2 variables

Question 45

what is inferential correlation?

Answer 45

-r is used to test population correlations, rho (ρ) H0 : ρ = 0 HA : ρ ≠ 0

Question 46

what is a t-test?

Answer 46

-Testing for differences between 2-group means -Can be used when there are two independent groups (i.e. experimental versus control; or pre- and post-scores for a group of the same people) OR paired (2 measurements from the same person over different time pts or paired participants together) H0 : µA = µB H0 : µX1 = µX2 HA : µA ≠ µB HA : µX1 ≠ µX2

Question 47

what test do you use when testing the mean differences with 3 or more groups?

Answer 47

analysis of variance (ANOVA)

Question 48

what is a one-way ANOVA?

Answer 48

sum of squares between groups and within groups for 3+ groups on 1 IV (Example: Burnout survey scores across different patient care units)

Question 49

what is a two-way ANOVA?

Answer 49

3+ groups on 2 IV; main effects versus interaction effects (see Prof KTs thesis example = SNP genotype by race)

Question 50

what is a repeated measures ANOVA?

Answer 50

3+ groups over repeated times F-ratio statistic: are omnibus tests—they only tell you a difference exists, not where the difference is located: H0 : µA = µB = µC HA : µA ≠ µB ≠ µC

Question 51

t/f - If significant p-values are obtained, post-hoc tests (multiple comparison procedures) are used to examine where group differences are occurring

Answer 51

true

Question 52

A researcher hypothesized that there would be no difference in respiratory rates for patients who self-administered respiratory treatments compared to respiratory treatments administered by a health care provider. Which would be the most appropriate statistical test? ``` Paired (dependent) t test Pearson’s r Mann Whitney U Independent (Student’s) t test None of the above ```

Answer 52

Independent (Student’s) t test RATIONALE: Dependent variable is respiratory rates, which is interval level data and 2 groups are being compared one time only.

Question 53

Capillary blood glucose levels were studied in four groups of patients with diabetes who had varying social support systems. Fasting glucose levels were obtained for each group member using a calibrated glucose meter. Subsequently, the mean glucose levels for the groups were compared. ``` Student’s (Independent) t test Paired (Dependent) t test Kruskal Wallis Pearson’s r ANOVA ```

Answer 53

ANOVA RATIONALE: Dependent variable is glucose level, which is interval level data and 4 groups are being compared or measured one time only.

Question 54

An investigation was undertaken to determine if there was a relationship between the quantity of coronary artery blockage and cholesterol levels in obese Caucasian males undergoing cardiac catheterization during January of 2013. The results indicate a strong positive correlation, r = .88, p = .001. What statistical test would you suspect was used to analyze these data? a. Spearman Rho correlation test b. Independent t test, also called the Student’s t test c. Pearson’s Correlation d. Mann-Whitney U test e. Repeated measure ANOVA

Answer 54

c. Pearson’s Correlation