Week 8 - Inferential Stat Methods Flashcards
what is inferential stats?
- 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.
t/f - Even if it’s a random sample, it’s rarely identical to the real population
true
what is sampling error?
tendency for statistics to fluctuate from one sample to another; the challenge is how to decide whether estimates are good population parameters?
what is sampling distribution of the mean?
a theoretical distribution of a test statistic (i.e., mean) from an infinite number of samples as data points.
what is a standard error of the mean (SEM)?
standard deviation (SD) of a sampling distribution of the mean (i.e. estimated from the sample’s SD and the sample size)
what happens in a normally distributed population…
- 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
what are the two forms of statistical inference?
- estimation of parameters (not as common in nursing research)
- statistical hypothesis testing
what is an example of estimation of parameters (trying to estimate for the entire population)?
- 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
what is an example of hypothesis testing (for a particular sample or group)?
- Impact of investigational drug compared to placebo on BP
- Impact of nursing intervention to prevent burnout and turnover
what are the two forms of parameter estimation?
- point estimation
- interval estimation
what is point estimate (as a form of parameter estimation)?
calculating a single statistic (i.e. sample mean) to estimate the population parameter (i.e. population mean)
what is interval estimation (as a form of parameter estimation)?
calculating a range of values the parameter (i.e. population mean) has a specified probability of being located
what is the confidence interval?
95-99%
what is confidence limits (CL)?
the range of values for the population and the probability of being right with a certain degree of confidence (i.e. 95% or 99%).
what are things to keep in mind about binomial distribution?
- 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
what are the typical CI proportions constructed on a binomial distribution?
ARR = absolute risk reduction RRR= relative risk reduction OR = odds ratio NNT = number needed to treat
what is hypothesis testing?
-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
what is the simplest way to decrease type ll error?
increase the sample size
t/f - making decisions to decrease type l error decreases the risk of type ll error
false - making decisions to decrease type l error increases the risk of type ll error
what is type l error?
- 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
what is type ll error?
- accepting the H0 when it should be rejected (false negative)
- Risk of Type II Error is controlled by setting power (1-β) at 80%
t/f - There is no “almost” significant at p=0.06
true
researchers compute a test statistic with their data for what reason
determine whether the statistic falls beyond the critical region in the relevant theoretical distribution
what is bivariate tests?
analysis of 2 variables to assess the empirical relationship between them
what is a non-significant result?
means that the relationship is from chance fluctuations (accept H0)
what is a significant result?
means that the H0 is very improbable and thus statistically significant (reject H0 and accept Ha)
what is normal theoretical probability distributions?
Each test statistic has its own mathematic proportions for calculating critical value-limit scores falling within normal theoretical probability distributions.
what are examples of normal theoretical probability distributions?
- t Distribution for t-tests
- F Distribution for ANOVA tests
- χ2 Distribution
- r Distribution
what is a two-tailed test?
Hypothesis testing in which both ends of the sampling distribution are used to define the region of “improbable” values.
what are the pros of two-tailed tests?
you do not need to know in advance the alternative hypothesis
what are the cons of two-tailed tests?
you may not be able to detect small differences
what is a one-tailed test?
Critical region of improbable values is entirely in 1 tail of the distribution—corresponding to the direction of the hypothesis set by the researcher
what is a pro of one-tailed test?
offers you more power to detect small differences
what are the cons of one-tailed test?
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)
what does the sampling distribution look like for two-tailed tests?
5% of the sampling distribution is equally split b/t 2 tails: 2.5% on each side
what is the sampling distribution of a one-tailed test?
5% of the sampling distribution is on 1 side
what are parametric stats?
- 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
what are non-parametric stats?
- 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
what is a bonferroni correction?
- designate a more conservative α threshold = p-value/# of total tests; 0.05/6 = 0.0083
- reduces type l error
what falls under the category of parametric (interval or ratio)?
- 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)
what falls under non-parametric (highly skewed or non-interval, non-ratio) tests?
- Mann-Whitney U test
- Wilcoxon signed ranks test
- Kruskal Wallis
- Friedman Test
- Spearman Rank Correlation (phi coefficient)
what is a chi-square test?
- 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
what is pearson’s r (correlation)?
- 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
what is descriptive correlation?
summarizes the magnitude of relationship b/t 2 variables
what is inferential correlation?
-r is used to test population correlations, rho (ρ)
H0 : ρ = 0
HA : ρ ≠ 0
what is a t-test?
-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
what test do you use when testing the mean differences with 3 or more groups?
analysis of variance (ANOVA)
what is a one-way ANOVA?
sum of squares between groups and within groups for 3+ groups on 1 IV (Example: Burnout survey scores across different patient care units)
what is a two-way ANOVA?
3+ groups on 2 IV; main effects versus interaction effects (see Prof KTs thesis example = SNP genotype by race)
what is a repeated measures ANOVA?
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
t/f - If significant p-values are obtained, post-hoc tests (multiple comparison procedures) are used to examine where group differences are occurring
true
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
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.
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
ANOVA
RATIONALE: Dependent variable is glucose level, which is interval level data and 4 groups are being compared or measured one time only.
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
c. Pearson’s Correlation
