Skills for biomedical science

What is the formula involving moles, concentration and volume?

moles = concentration x volume

What is the formula involving mass, moles and molar mass?

mass = moles x molar mass

What should a good hypothesis statement include?

• contain if and a then

• be testable by an experiment

• Be based on information in prior research

• Include both the independent (cause) and dependent (effect) variables

What is the difference between the Null hypothesis and the alternate hypothesis?

Null - there is no difference, effect or relationship in the population, any difference we see is due to chance

• the drug has no effect on blood pressure

Alternate - it says there is an effect, difference or relationship.

• the drug does affect blood pressure

What is numerical data?

data that can be measured or counted as numbers.

• discrete - whole number counts only, example number of hospital visits, number of seizures per month

• continuous - can take any value on a scale and can be measured on a infinite scale including decimals, example height, weight, body temperature

What is categorical data?

data that falls into groups or labels

• nominal - categories with no natural order, examples blood groups, sex disease

• ordinal - categories with meaningful order but gaps between them aren’t equal or measurable, examples cancer stage, pain score

How can you turn numerical data into categorical data?

You take a continuous measurement and sort it into groups using cut-off points.

Numerical variable	Cut-offs	Categorical result
BMI (kg/m²)	<18.5, 18.5-24.9, 25-29.9, ≥30	Underweight / Normal / Overweight / Obese (ordinal)
Systolic BP (mmHg)	≥140 or <140	Hypertensive / Not hypertensive (binary)
Age (years)	0-17, 18-64, 65+	Child / Adult / Older adult (ordinal)
HbA1c (mmol/mol)	<42, 42-47, ≥48	Normal / Pre-diabetes / Diabetes (ordinal)

Explain frequencies and proportions?

frequencies - number of times a value or category occurs

proposition - fraction of the total that falls into a category

proportion = number in a category / total number x 100 (if expressed as a percentage)

How to calculate the mean, median and mode?

Mean = sum of all values ÷ number of values

Median = Put the values in order, then pick the middle one.

Mode = The value that occurs most often.

What is the variance?

how spread out the data is around the mean

1. calc how far each value is from the mean

2. square those differences

3. find their averages

Example:
Data = 2, 4, 6
Mean = 4

Differences from mean:

• 2 − 4 = −2 → squared = 4

• 4 − 4 = 0 → squared = 0

• 6 − 4 = 2 → squared = 4

Variance = (4 + 0 + 4) / 3 = 2.67

What is standard deviation?

the typical amount that individual values differ from the mean. (the square root of the variance). it tells you how spread out the individual measurements are.

Imagine 5 patients' blood pressures. The mean is the middle point, and the SD tells you how far the patients are from that middle, on average.

• Small SD: everyone is close to the average (e.g. 128, 130, 131, 129, 132)

• Large SD: people are all over the place (e.g. 100, 160, 120, 145, 125)

What Is standard error?

how much can I trust my average? how precisely your sample mean estimates the true population mean

• Small SE: your sample mean is probably close to the true population mean

• Large SE: your sample mean could be well off

The key point: a bigger sample gives a smaller SE, because more people means a more reliable average.

In one line: SE describes how accurate your average is.

What is the range?

maximum - minimum value gives the range.

What effects the range?

outliners hugely affect the range because one extreme value changes it completely

What is the interquartile range?

how spread out is the middle half of the data.

IQR = Q3 − Q1

• It ignores the lowest 25% and highest 25%, so outliers have little effect

• It's the spread that goes with the median

example

systolic BP (mmHg) in 7 patients, in order: 120, 125, 130, 130, 135, 140, 190

1. Range = 190 − 120 = 70 mmHg

2. Median = the 4th value = 130

3. Q1 = the middle of the lower half (120, 125, 130) = 125

4. Q3 = the middle of the upper half (135, 140, 190) = 140

5. IQR = 140 − 125 = 15 mmHg

What is correlation?

measures how strongly 2 numerical variables are related. (move together)

important to know that correlation does not mean causation.

Explain correlation co efficient?

The correlation coefficient (r)

A single number between −1 and +1:

r value	Meaning
+1	Perfect positive: as one rises, the other rises in a perfect straight line
0	No linear relationship
−1	Perfect negative: as one rises, the other falls in a perfect straight line

Explain Pearsons correlation?

this shows you how strongly 2 variable are related and whether they move in the same or opposite direction

−1 to +1.
+ = variables increase together
− = one increases as the other decreases
0 = no linear relationship.

Asdumptions of pearsons correlation?

• Data from both variables follow normal distributions

• Your data have no outliers

• Your data is from a random or representative sample

• You expect a linear relationship between the two variables

Explain R - Correlation Coefficient?

r is a single number that tells you how strongly two numerical variables are linked in a straight-line way, and in which direction.

1. Direction (the sign)

• Positive (+): as x goes up, y goes up

• Negative (−): as x goes up, y goes down

2. Strength (the size, ignoring the sign)

The closer to 1 (or −1), the tighter the dots hug a straight line. The closer to 0, the more of a shapeless cloud.

The scale

r	What the scatter plot looks like
+1	Dots on a perfect upward line
+0.8	Strong upward trend, a little scatter
+0.4	Loose upward trend
0	No pattern at all
−0.4	Loose downward trend
−0.8	Strong downward trend
−1	Dots on a perfect downward line

Rough strength guide (cut-offs vary by textbook):

• 0 to 0.3: weak

• 0.3 to 0.7: moderate

• 0.7 to 1: strong

What does monotonic mean?

The pattern only ever goes up, or only ever goes down, and never turns around.

The three graphs show this:

1. Monotonic (left): the dots trend steadily downward

2. Monotonic (middle): the dots trend upward, but in a curve (slow at first, then steep). It's still monotonic, because it never goes back down

3. Non-monotonic (right): the dots rise and then fall, like an upside-down U. The direction reverses, so Spearman's isn't suitable here

Explain Pearsons vs spearman's correlation?

• Pearson's measures straight-line (linear) relationships

• Spearman's measures one-direction (monotonic) relationships

Explain homoskedastic and heteroskedastic?

this measures consistency across relationships.

homo = The spread of the points is roughly the same across the graph. The variability remains constant

hetero = the spread of the points changes as X increases. the variability gets larger or smaller