Experimental and data skills

The single factor you deliberately **change** (manipulate) — the cause you are testing. Plotted on the **x-axis**.

The factor you **measure** as the outcome; it **depends on** the independent variable. Plotted on the **y-axis**.

A factor kept **constant** in every trial so it cannot affect the result — this keeps the test **fair**.

A **controlled variable** is a factor held **constant**. A **control treatment** is a whole **baseline run** with the tested factor **absent**, used for comparison.

If two things change together you get a **confounding variable** — you can't tell which factor caused the result, so the test is **invalid**.

$\%\ \text{change} = \dfrac{\text{final} - \text{initial}}{\text{initial}} \times 100$. Use the **control** value as the 'initial'.

**Specifically**, with its quantity (e.g. 'temperature at 22 °C', 'volume of solution'), never 'keep everything the same'.

$R_f = \dfrac{\text{distance moved by the pigment}}{\text{distance moved by the solvent}}$ — both measured from the start line. It has **no units** and is always between **0 and 1**.

Rf = 45 ÷ 90 = **0.50** (no units, because it is a ratio of two lengths).

The one that travels **furthest** — it has the **highest Rf**. The lowest Rf is the least soluble.

Count in several quadrats, take a **mean per quadrat**, find the **density (number per m²)**, then **scale up** to the total habitat area. Using a mean of many quadrats improves reliability.

It separates **DNA fragments by SIZE**: DNA is negatively charged, so an electric field pulls it through the gel and the **smallest fragments travel furthest**.

**PCR** amplifies (copies) DNA; a **respirometer** measures respiration rate (oxygen used per unit time).

A **replicate** is one repeat of the same measurement. Several let you take a **mean** (reducing random error), **spot anomalies**, and check the result is **repeatable**.

**Repeat each measurement more times and take the mean.** More replicates even out random error and make an anomaly stand out.

$\bar{x} = \dfrac{\sum x}{n}$ — add the readings and divide by how many there are. The spread (range $=$ max $-$ min, or the standard deviation) shows how reliable the repeats are: small spread = reliable.

**Reliable** = repeats of the same method agree. **Valid** = a fair test of the claim (a control + only one variable changed). **Accurate** = close to the true value.

It sits **far outside the other repeats**. You re-check it or leave it out of the mean — which is only possible because you took several repeats.

State **what the data show** (e.g. the means differ), then **weigh it against the limitations** (small sample, big spread/overlap, no control) for a **balanced** judgement.

A **fix PLUS a matched reason** — e.g. 'more replicates **so the mean is more reliable**' or 'add a control **so the effect is shown to be due to the variable**'. A bare fix scores half.

$M = \dfrac{\text{image size}}{\text{actual size}}$ — both in the **same unit**. It's a ratio, so it has **no units** (write $\times N$).

Rearrange the triangle: $\text{actual} = \dfrac{\text{image size}}{M}$. Convert to one unit, then **divide the image size by the magnification**.

Measure the bar on the image (e.g. $40\text{ mm} = 40\,000\ \mu\text{m}$), read the real distance it represents (e.g. $80\ \mu\text{m}$), then $M = 40\,000 \div 80 = \times 500$.

**Multiply by 1000** ($1\text{ mm} = 1000\ \mu\text{m}$). Image lengths are in mm but cells are in µm — match units **before** dividing or you'll be 1000× out.

Real size = divisions × µm per division = $20 \times 2.5 = 50\ \mu\text{m}$.

An **eyepiece graticule**, calibrated against a **stage micrometer** (not a plain ruler).

Find the **x-value**, go **up to the curve**, **across to the y-axis**, read the height — and write it **with its unit**.

**Interpolate** = estimate a value **between** plotted points (safe). **Extrapolate** = predict a value **beyond** the data (a prediction — the trend may not hold).

Take roughly the **midpoint** of the neighbouring readings, e.g. $y \approx \dfrac{30 + 42}{2} = 36$ (with the unit).

**Direction first** (rises/falls), then the **change of pattern** (plateau or peak), each backed by **figures** from the graph.

At least **one similarity AND one difference** between the series, each supported by a **value** from the data.

A **reason** drawn from the trend — and you should flag it as a prediction (extrapolation), since the trend might change.

A value with **no unit** scores nothing — always quote the **unit** read from the axis.

$\% \text{ change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$ — always divide the CHANGE by the OLD value. A negative answer is a percentage decrease.

rate $= \dfrac{\text{change in quantity}}{\text{time}} = \dfrac{\text{rise}}{\text{run}}$ — the GRADIENT of the line. Take two points and divide; always write the units.

ratio = part ÷ whole, e.g. mitotic index $= \dfrac{\text{dividing cells}}{\text{total cells}}$. Can be a fraction, decimal, percentage or A : B.

**% change** = (new − old) ÷ old × 100 (how much it moved). **% of** = part ÷ whole × 100 (what share it is). Read which one the question asks.

range = largest value − smallest value.

A rate is a quantity PER unit time; without the unit (e.g. cm³ s⁻¹, breaths min⁻¹) it is incomplete and loses the mark.

$\bar{x} = \dfrac{\sum x}{n}$ — **add all the values and divide by how many there are** ($n$). The mean keeps the same units as the data.

**Mean** = add-up-and-divide average. **Median** = the **middle** value in order. **Mode** = the **most common** value (tallest bar on a frequency graph).

How **spread out** the data are around the mean. **Small s** = tightly clustered; **large s** = widely scattered. You find it on your GDC, not by hand.

The **spread** of the data — usually **± one standard deviation** about the mean. Its total height = 2s; a longer bar means more spread (less reliable).

Error bars **OVERLAP → difference NOT significant**. Error bars with a **clear gap (no overlap) → difference IS significant**.

**Median** = line inside the box; **box** = lower quartile (Q1) to upper quartile (Q3) = middle 50%; **whiskers** = min and max; a **separate point** = an **outlier**.

The **chi-squared (χ²) test** — it is for **counts/frequencies**, e.g. testing a 3:1 genetic ratio.

The **t-test** — use it to ask whether **two averages** are significantly different.

$\chi^2 = \sum \dfrac{(O-E)^2}{E}$ — where **O** = observed count, **E** = expected count; add one term per category.

Compare the **calculated** statistic to the **critical value** at **p = 0.05**: if **calculated ≥ critical**, it is **significant** (p < 0.05) → reject H₀.

**H₀**: there is **no** real difference/association (any difference is chance). **H₁**: there **is** a real difference/association.

That the means are **probably not significantly different** — a t-test would give t below the critical value (p > 0.05).

For **χ²**: (number of categories − 1). For a **t-test of two groups**: $df = n_1 + n_2 - 2$. The df picks the row of the critical-value table.

**Positive**: as one variable rises, the other **rises** (line slopes up). **Negative**: as one rises, the other **falls** (line slopes down).

It measures a linear correlation from **−1 to +1**: the **sign** = direction (+ together, − opposite) and the **size** (how close to ±1) = **strength**. $r ≈ 0$ = no linear relationship.

**$R^2 = r^2$.** It is the **fraction (or %) of the variation** in y explained by x. e.g. $r = 0.9 → R^2 = 0.81 →$ ~81% explained. Given R², $r = \pm\sqrt{R^2}$.

A **third (confounding) variable** or coincidence could cause both. Only a **controlled experiment** can establish that one variable causes a change in another.

State the **direction** (positive/negative correlation) **and** quote a **figure/comparison** from the data — not just 'there is a relationship'.

**Equally strong** — strength depends on $|r|$ (how close to 1), not the sign. They differ only in **direction**.

$D = \dfrac{N(N-1)}{\sum n(n-1)}$ — where $N$ = total individuals (all species) and $n$ = individuals of each species. Higher $D$ = more diverse (minimum 1).

$N = \dfrac{n_1 \times n_2}{n_3}$ — $n_1$ = marked & released, $n_2$ = second catch, $n_3$ = marked individuals in the second catch, $N$ = estimated total.

$N$ = the TOTAL number of individuals of ALL species added together; $n$ = the number of individuals of ONE particular species.

Because $D$ also depends on **evenness**. A community dominated by one species has a LOWER $D$ than one where individuals are spread evenly.

Marks don't harm the animals or change catchability; marked animals mix back fully; no births, deaths or migration between samples; marks aren't lost.

Sample the same site with the same method each year, calculate $D$ each time, and compare — a rising $D$ means biodiversity is increasing.