Statistics & Evidence-Based Practice

Question 1

What is the estimated incidence of accidental awareness in general anaesthesia according to NAP5?

Answer 1

1 in 20,000

Question 2

What is a Chi-squared test?

Answer 2

Non-parametric statistical hypothesis test that compares the frequency of observed results against the expected frequency if there were no difference between groups.

It is primarily used when examining categorical variables, and whether the difference between observed and expected frequencies are due to chance.

Question 3

What type of data is a student T-test used for?

Answer 3

It is a parametric test which may be used on continuous, quantitative data.

Question 4

State the main rules for logarithms.

Answer 4

• Multiplication becomes addition: log(xy) = log(x) + log(y).
• Division becomes subtraction: log(x/y) = log(x) – log(y).
• The reciprocal becomes negative: log(1/x) = -log(x).
• Power becomes multiplication: log(x^n) = n · log(x).
• Any log of its own base is one: log10(10) = 1.
• Any log of one is zero: log10(1) = 0.

NOTE: A logarithm is defined as the power (x) to which a base must be raised in order to produce a given number.

Question 5

Which statistical tests are used for parametric data?

Answer 5

• 2 groups, paired: Student’s paired t-test.
• 2 groups, unpaired: Student’s unpaired t-test.
• > 2 groups, paired: Paired ANOVA (analysis of variance).
• > 2 groups, unpaired: Unpaired ANOVA.

Question 6

Which statistical tests are used for non-parametric nominal data?

Answer 6

• 2 groups, paired: McNemar’s test.
• 2 groups, unpaired: χ² with Yates’ correction (Chi-squared).
• > 2 groups, unpaired: χ²

Question 7

What statistical tests are used for non-parametric ordinal data?

Answer 7

• 2 groups, paired: Wilcoxon signed rank.
• 2 groups, unpaired: Mann-Whitney U test.
• > 2 groups, paired: Friedman.
• > 2 groups, unpaired: Kruskal-Wallis.

Question 8

Outline the level of the hierarchy of evidence.

Answer 8

• Level 1a: systematic review or meta-analysis of one or more randomised controlled trials (RCTs).
• Level 1b: At least one RCT.
• Level 2a: At least one well-designed, controlled, non-randomised study.
• Level 2b: Cohort studies.
• Level 3: Case control studies or case series.
• Level 4: expert opinion.

Question 9

What is a Bland-Altman plot?

Answer 9

Provides a method of comparing two methods of measurement and establishing their degree of agreement.

Question 10

What does a Forest plot show?

Answer 10

Provides a visual representation of effect size for individual studies within a meta-analysis.

Question 11

What does a funnel plot show?

Answer 11

Used to visually inspect for evidence of reporting bias.

Question 12

What percentage of results lies within 1, 2 and 3 standard deviations of the mean?

Answer 12

1: 68.2%
2: 95.4%
3: 99.7%

Question 13

How do the mean, median and mode compare in positively skewed data?

Answer 13

Mode < Median < Mean

Question 14

What is the equation of number needed to treat?

Answer 14

ARR = incidence in control group – incidence in treatment group

The number needed to treat is 1/ARR

Question 15

Define variance and how it relates to standard deviation.

Answer 15

The average of the squared deviations from the mean.

Standard Deviation (s) = the square root of the variance

Question 16

Outline the phases of clinical trials.

Answer 16

• Phase 1: 20-50 healthy volunteers. This phase examines pharmacokinetic and pharmacodynamic effects.
• Phase 2: 50-300 volunteers. Further pharmacokinetic and pharmacodynamic effects. Examination of different drug doses and frequencies.
• Phase 3: 250-1000+ volunteers. Randomised controlled trials comparing the drug with current treatments and assessment of frequent side effects.
• Phase 4: Post marketing surveillance of rare side effects.

Question 17

What is the difference between accuracy and precision?

Answer 17

Accuracy is the ability of a measuring device to record the actual value being measured, i.e. how close to the bullseye is an arrow.

Precision is the reproducibility of repeated measurements and how spread out they are, i.e. how tightly packed are a group of fired arrows (regardless of where they hit the target).

Question 18

What effect does decreasing the alpha in a statistical power calculation have on the beta value and power?

Answer 18

Decreasing α increases β (and reduces power) if sample size and effect size stay the same, because you’re making it harder to detect a true effect by setting a more conservative threshold.

This leads to a lower power because power = 1 - beta

Question 19

What kind of graph would x being inversely proportional to y generate?

Answer 19

Rectangular hyperbola
x is proportional to 1/y

Question 20

What is the difference between ‘interval’ and ‘ratio’ in the context of quantitative data?

Answer 20

Interval: 0 is in the middle (e.g. centigrade)

Ratio: has a true zero that it cannot drop below (e.g. Kelvin)

Question 21

Define 95% confidence interval in terms of standard error of the mean.

Answer 21

95% CI = Mean +/- 1.96 SEM

Question 22

When should Fisher’s exact test be used instead of Chi squared?

Answer 22

Data are in a 2 x 2 table and at least one cell has an expected frequency of < 5

(especially in small sample sizes)

Question 23

What is the equation for a confidence interval?

Answer 23

Mean ± Z*(Standard Error)

Z = the Z-score corresponding to the desired confidence level.

This formula helps estimate the range in which a population parameter lies based on sample data.

Question 24

What are the different types of measurement error?

Answer 24

OFFSET ERROR

• lines are linear and parallel to actual values but fixed amount is added or subtracted
• needs one-point calibration (e.g. zeroing art line)

GAIN ERROR

• gradient of line increases or decreases
• needs two-point calibration (e.g. pH electrode)

Question 25

What is **drift** with regards to measurement error?

Answer 25

Loss of accuracy over time (may result in an offset or gain error).

Question 26

What's the **difference** between interval and ratio data?

Answer 26

**INTERVAL**: numerical scale with equal intervals and no absolute zero (e.g. celsius) **RATIO**: numerical scale with equal intervals and an absolute zero (e.g. Kelvin, weight)

Question 27

What are the **ways** in which spread can be demonstrated for non-parametric data?

Answer 27

* Range * Interquartile range

Question 28

Outline the **hierarchy of evidence**.

Answer 28

* **Level 1a**: systematic review or meta-analysis of one or more randomised controlled trials (RCTs). * **Level 1b**: At least one RCT. * **Level 2a**: At least one well-designed, controlled, non-randomised study. * **Level 2b**: Cohort studies. * **Level 3**: Case control studies or case series. * **Level 4**: expert opinion.

Question 29

What's the **difference** between quantitative and qualitative data?

Answer 29

* **Quantitative**: numerical data that can be measured. * **Qualitative**: descriptive data that can be observed but not measured.

Question 30

What **correlation coefficient** is suggestive of a strong association?

Answer 30

0.6-0.79 ## Footnote NOTE: 'r' is used to denote correlation coefficients.

Question 31

What is the **standard error** of the mean?

Answer 31

Estimate of how much the sample mean is expected to vary from the true population mean. SEM = σ/√n ## Footnote σ is the standard deviation of the population n is the number of samples

Question 32

What is the **difference** between **discrete** and **continuous data**?

Answer 32

* **Discrete data**: specific, separate values (often counts or whole numbers). * **Continuous data**: any value within a range (infinitely subdivided).

Question 33

# Define: statistical power

Answer 33

The probability that a statistical test correctly rejects a null hypothesis (i.e. detects a real effect when one truly exists). Power = 1 − β ## Footnote β is the probability of a type 2 error

Question 34

What are **type 1 and type 2** errors?

Answer 34

* Type 1 (alpha error): **incorrectly rejecting** the null hypothesis when it is true (concluding that there is a difference when there isn't) * Type 2 (beta error): **failing to reject** a null hypothesis (concluding that there is no difference when there is a difference)

Question 35

What is the **p** value?

Answer 35

The probability of obtaining the observed results (or more extreme) if the null hypothesis were true.

Question 36

What is a **confidence interval**?

Answer 36

A range of values within which the true population parameter is expected to lie with a certain level of confidence (usually 95%).