Week 5

Question 1

Quantitative data: Identifying the appropriate classification scheme for variables can help determine what?

Answer 1

what types of statistical methods are appropriate for describing data or for making inferences.

Question 2

Quantitative data: Identifying the appropriate classification scheme for variables can help determine what types of statistical methods are appropriate for describing data or for making inferences. Give 2 examples of these schemes and describe

Answer 2

1) Discrete
Variables have a “yes” or “no” value
Alive or dead
Number of hospitalizations
2) Continuous
Infinite number of values within a given range
Age
Body weight

Question 3

What are the exceptions to quantitative data rules?

Answer 3

Exceptions to the rules:
Ordinal data may imply an underlying continuous scale when large numbers of categories are present.
Example: using a pain scale of 0 – 100
Interval/ratio data may be discrete if the variable can only take on integer values.

Question 4

List 3 measures of central tendency (Quantitative Data)

Answer 4

Mean – average; applicable with interval and ratio values
Median – represents central tendency better than mean if outliers are present
Mode – not commonly used in clinical research

Question 5

List and describe some measures of dispersion (Quantitative Data)

Answer 5

Range – difference between the lowest value in the data from the highest value in the data
Interquartile range (IQR) – restricted to values that lie within the middle 50% of the distribution
Variance – how far the values of a variable lie from the mean
Standard deviation – square root of variance
Coefficient of variation – standard deviation / mean
Skewness – indicates that the data are not evenly distributed around the mean, in other words, more of the data are concentrated to either the right or the left of the mean value and the “tail” on the opposite side of the mean is longer

Question 6

Quantitative Data: List some ways to organize and visualize

Answer 6

Tables: Frequency table
Plots: Box & whisker plot
Graphs
Charts: Bar Chart, Pie Chart

Question 7

Describe box and whisker plots

Answer 7

IQR = box = middle 50% of the distribution
Median noted by line in the middle of the box
Minimum and maximum values noted by whiskers
Mean noted by diamonds
Useful when making comparisons across different groups that may not have equivalent underlying distributions

Question 8

Data: Define rates and give examples

Answer 8

Proportions over a specific time-period with a base (multiplier)
Morbidity and mortality
Incidence and prevalence

Question 9

Describe morbidity and mortality rates

Answer 9

1) Centers for Disease Control and Prevention’s National Center for Health Statistics Data:
-2,437,163 deaths in the United States in 2009
-US population of 307,024,820 yields a mortality rate of 793.8 deaths per 100,000 population in the United States in 2009

Question 10

Define incidence and prevalence

Answer 10

1) Incidence: measures the risk of developing an outcome
2) Prevalence: measures the probability of having an outcome
-More appropriate to say “point prevalence” compared to “prevalence rate” since this is a proportion and not a rate

Question 11

True or false: You can’t have a test that’s 100% specific and 100% sensitive

Answer 11

True

Question 12

Describe diagnostic data

Answer 12

1) How do you truly identify patients that have an outcome (true positive) and avoid detection of an outcome in patients that do not have it (false positive)?
2) Sensitivity (true positive rate)
3) Specificity (true negative rate)
1 – false positive rate = specificity (true negative rate)
4) Most tests used to diagnose diseases have a sensitivity of 80% and specificity of 90%
-Sensitivity is gained at the expense of specificity and vice versa
-Receiver operating characteristic curves further define this tradeoff

Question 13

Describe

Answer 13

The area under the curve for ROC-1 is closer to 1 and further from the chance diagonal. It would identify a larger number of true positives.

Point A: larger proportion of patients with the outcome are detected and there are more false positives

Point B: detects less true positives and less

Question 14

Diagnostic data: Describe the ADA Standards of Care (2022)

Answer 14

Is a BMI > = 25 kg / m2 an appropriate risk factor for diabetes for all ethnicities?
“…BMI cut points fall consistently between 23 and 24 kg/m2 (sensitivity of 80%) for nearly all Asian American subgroups (with levels slightly lower for Japanese Americans).”
“An argument can be made to push the BMI cut point to lower than 23 kg/m2 in favor of increased sensitivity; however, this would lead to an unacceptably low specificity (13.1%).”

Question 15

Describe Normal distribution (bell curve)

Answer 15

1) z distribution / z scores
-Mean = 0
-SD = 1
-Continuous variables
2) t distribution / student’s t distribution
-Modification to the standard normal distribution (or z distribution) when the sample size is relatively small
-Useful whenever the actual population standard deviation is not known or when a good estimate is not available
-Continuous variables

Question 16

Statistical Distribution (other than standard distr.); describe:
1) Binomial distribution
2) F distribution
3) Poisson distribution
4) Gamma distribution

Answer 16

1) Mutually exclusive categories of data
2) Analysis of variance (ANOVA) and linear regression analysis
3) Useful for detecting rare outcomes
4) Variable of interest is interval or ratio but is very highly skewed

Question 17

Stat. distribution: List the 3 main bullet points of the Central limit theorem

Answer 17

1) The mean of all sample means will equal the population mean
2) The standard deviation of the sampled means is equal to the standard error of the mean
3) As the sample size increases, the distribution of the sample means will approach a normal distribution regardless of the underlying distribution of the variable

Question 18

Define and describe Statistical inference. When are latin or greek letters used?

Answer 18

1) Process of analyzing data from a sample and using those results to infer the related values in the source or target population
2) Data related to the population of interest are referred to as parameters and are usually represented by Greek letters
3) Data from a sample is referred to as a statistic and is represented by Latin letters

Question 19

Inference:
1) Define stat. estimation
2) Define hypothesis testing

Answer 19

1) Process by which estimates of the population parameters are generated from sample statistics with a focus on generating precise estimates with minimal bias
2) Making a conclusion about a hypothesized difference or relationship using observations from the sample

Question 20

Inference: Define and describe Statistical estimation

Answer 20

1) Mean, median, and standard deviation are basic examples of estimation
2) Point estimation: One single value is estimated for the statistical quantity of interest (e.g., mean)
3) Interval estimation
-Confidence intervals
-Inference of the precision of an estimate

Question 21

Hypothesis testing: What makes a good hypothesis?

Answer 21

Declarative
Describes a relationship between two or more variables

Question 22

Hypothesis testing: What is the Null hypothesis (HO)? Describe

Answer 22

1) No relationship or no difference between the variables of interest
2) Conclusions of studies are made with respect to the null hypothesis
Reject
Fail to reject

Question 23

Hypothesis testing: what is the opposite of the null hypothesis?

Answer 23

Alternative hypothesis (HA)

Question 24

Hypothesis testing: What are the 2 types of errors? What do they have in common?

Answer 24

Type I error (α)
Type II error (β)
Both of these errors represent quantities that the researcher sets acceptable levels for when designing the study before (ad hoc) data are analyzed.

Question 25

Inference: Hypothesis testing: Describe Nondirectional tests

Answer 25

1) Two-sided or two-tailed 2) Comparing means between two groups 3) Difference Null hypothesis = no difference between variables (i.e., control vs. placebo) If α = 0.05, 2.5% will be distributed to each side / tail 4) Equivalence Null and alternative hypotheses must be “reversed” compared to a test of difference Assess using two one-sided statistical tests If α = 0.05, then CI = 90% for equivalence testing

Question 26

Inference: Hypothesis testing: Describe directional tests

Answer 26

One-sided or one-tailed Comparing means between two groups Superiority Non-inferiority

Question 27

List 3 approaches to hypothesis testing

Answer 27

Traditional testing Confidence intervals Bayesian approach

Question 28

Describe the steps of traditional hypothesis testing

Answer 28

Step 1: Convert research question into null and alternative hypothesis Step 2: Select appropriate statistical test Step 3: Select α Step 4: Calculate test statistic Step 5: Draw a conclusion

Question 29

Describe step 1 of traditional hypothesis testing

Answer 29

Step 1: Convert research question into null and alternative hypothesis Look closely to see whether two-sided or one-sided statistical tests were used to determine if the hypothesis testing approach was directional or nondirectional since research questions may be stated as directional Two-sided approach is more conservative

Question 30

Describe step 3 of traditional hypothesis testing

Answer 30

Ad hoc 0.05 or 5% is standard

Question 31

What step of traditional hypothesis testing do computers do?

Answer 31

Step 4: Calculate test statistic

Question 32

Describe step 5 of traditional hypothesis testing and give an example

Answer 32

1) p-values: if less than ad hoc α, you would consider the results statistically significant 2) Example p = 0.027 and α = 0.05 This means that there is a 2.7% chance (probability) of finding a result of this magnitude (or larger) assuming the null hypothesis is true Smaller p-values indicate increasingly strong evidence against the null p = 0.45 does not suggest strong evidence against the null while p = 0.001 would denote strong evidence against the null hypothesis p-value does not indicate strength or size of finding

Question 33

Hypothesis testing: Describe Confidence intervals

Answer 33

1) No difference between variables = 1 2) If the interval contains the null value of interest, then the null hypothesis is not rejected at a given significance level 3) If the interval does not contain the null value, the null is rejected at a given significance level

Question 34

Bayesian hypothesis testing is not __________ used in biomedical literature

Answer 34

commonly

Question 35

Bivariate Analysis: 1) What is it? 2) What does it look at?

Answer 35

1) Analysis with just two variables 2) Looking at outcomes between two groups (control and experimental

Question 36

Give a hypothetical example of a study with bivariate analysis

Answer 36

1) “Randomized controlled trial: effect of standards of care with exercise compared to standards of care without exercise on hemoglobin glycation for patients with type two diabetes mellitus.” -Null hypothesis – there is not difference in HbA1c results between the group exercising and the group not exercising P – patients with type II DM at your healthcare facility I – exercise + standards of care C – standards of care O – HbA1c

Question 37

Describe Bivariate analysis

Answer 37

1) Independent variable is discrete (nominal) Standards of care Standards of care + exercise 2) Dependent variable is continuous (ratio) 3) Use nondirectional statistical test Null hypothesis says there is no difference between groups 4) Preferred test is independent groups t-test; tests the differences in the means of two groups.

Question 38

Describe the types of continuous data

Answer 38

Question 39

Bivariate analysis: What if we had three arms in our study? Like: Standards of care Standards of care + exercise Standards of care + diet counseling

Answer 39

Analysis of variance (ANOVA) is useful to compare the means of three groups An ANOVA used to compare two groups would produce the same results as a nondirectional t-test

Question 40

What if we want to compare the proportions (nominal data) of patients at goal for two groups (standards of care & standards of care + exercise)?

Answer 40

1) Use chi-square test of homogeneity; nondirectional test of difference of proportions; will see 2x2 contingency tables to analyze data Can also be used to look at proportions of two or more groups 2) Use Fisher exact test if sample size is too small How do I know if sample size is too small?

Question 41

Describe the types of discrete data

Answer 41

Question 42

Example of bivariate analysis: What if you want to compare standards of care to standards of care + diet counseling + exercise? And now, you want to measure baseline A1c and A1c at the end of the study.

Answer 42

1) If the comparison groups used for the statistical comparison involve more than one measurement on the same patients, then the groups are considered dependent (the sets of observations are said to be paired) 2) The test statistic for comparing baseline to posttreatment involves differences in means between dependent groups; therefore, a dependent groups or paired t-test is used 3) If you have more than two groups, you can use repeated-measures ANOVA

Question 43

HBA1c is __________ data. If you're just looking at end results, is it paired?

Answer 43

continuous; unpaired

Question 44

Give 2 examples of additional statistical tests for bivariate analysis

Answer 44

Wilcoxon-Mann-Whitney Study differences between two independent groups on a variable that has an ordinal level of measurement Kruskal-Wallis Extends the Wilcoxon-Mann-Whitney test to more than two groups when the groups are independent

Question 45

Bivariate analysis: How do you determine if the drop in A1c is a response associated with the amount of time spent exercising?

Answer 45

1) Pearson correlation coefficient (r) -Measure of how two variables are linearly related for continuous data -A coefficient of + 1 indicates a perfect positive linear relationship between the two variables -A coefficient of -1 indicates that there is perfect negative linear correspondence between the two variables -An r of 0 means that there is no overall linear relationship between two variables

Question 46

Bivariate Analysis: Describe the Spearman rank correlation coefficient

Answer 46

Very similar to Pearson interpretation Can be used with interval and ratio data after transformation into ranks

Question 47

Bivariate Analysis: The primary factors used to determine which statistical test to use are?

Answer 47

1) Independence or dependence of the groups (samples) 2) Level of measurement of the dependent (outcome) variable 3) Assumptions on which specific statistical tests are based

Question 48

Quantitative: List and describe 2 kinds of continuous data

Answer 48

1) Interval data: body temperature; a change in 1 degree in either direction is the same defined interval; 80 degrees F is not twice as hot as 40 degrees F Ranked data with meaningful difference between numbers and no defined zero 2) Ratio data: body weight; a change in 1 pound in either direction is the same defined interval; 80 pounds weighs twice as much as 40 pounds Interval data with defined zero

Question 49

Give 2 kinds of discrete data (Quantitative)

Answer 49

1) Nominal data: dead or alive 2) Ordinal data: Likert-scales -Ranked data

Question 50

US population of 307,024,820 yields a mortality rate of _________ deaths per 100,000 population in the United States in 2009

Answer 50

793.8

Question 51

Incidence and prevalence: ADA Standards of Care 2022 “The prevalence of ________________ therapy in hospitalized patients can approach 10%, and these medications can induce hyperglycemia in patients with and without antecedent diabetes.”

Answer 51

glucocorticoid

Question 52

Differentiate sensitivity and specificity

Answer 52

Sensitivity (true positive rate) Specificity (true negative rate)

Question 53

Give the highlights of ADA Standards of Care (2022)

Answer 53

1) “…BMI cut points fall consistently between 23 and 24 kg/m2 **(sensitivity of 80%)** for nearly all Asian American subgroups (with levels slightly lower for Japanese Americans).” 2) “An argument can be made to push the BMI cut point to lower than 23 kg/m2 in favor of increased sensitivity; however, this would lead to an unacceptably **low specificity (13.1%)**.”

Question 54

Central limit theorem says what?

Answer 54

As you increase the population, you get closer to the true population parameter

Question 55

One generally accepted rule of thumb is a sample size of at least _____ is sufficiently large as long as there are only moderate departures from the normal distribution.

Answer 55

30 (ppl)

Question 56

What is a type 1 error? What do you look at?

Answer 56

Type I error (α) Rejecting the null hypothesis when the null hypothesis is true P values

Question 57

Define P values and describe

Answer 57

p-values Probability of finding the results of the study (or more extreme results); assuming the null hypothesis is true The smaller the p-value than the less likely the result occurred by random chance The level of confidence for a given study is generally related to the type I error rate such that the confidence level is one minus the type I error rate, or 1 – α. Thus, a type I error rate of 0.05 (or 5%) leads to a 95% confidence level.

Question 58

Describe type 2 errors? What do you look at?

Answer 58

1) Type II error (β): Failing to reject the null hypothesis when the null hypothesis is false 2) Power: Probability of rejecting the null hypothesis given that the null hypothesis is actually false Tells us the likelihood of being correct Typical values for the type II error rate are 20% and 10%, which translate to power levels of 80% and 90%, respectively

Question 59

Step 5 of trad. hypothesis testing: Draw a conclusion: p-values: if less than ad hoc α, you would consider the results statistically _____________

Answer 59

significant

Question 60

Inference: Significance: Differentiate between statistical and clinical significance

Answer 60

1) Statistical: p-values 2) Clinical -Will the results of a study change how you practice? -A study can have statistical significance and no clinical significance -A study cannot have clinical significance if it does not have statistical significance -NNT and NNH are commonly considered in determining clinical significance

Question 61

True or false: A study cannot have clinical significance if it does not have statistical significance

Answer 61

True

Question 62

Describe the types of continuous data

Answer 62

Question 63

Describe the types of discrete data

Answer 63