Overview of statistical tests (with links)

Link to ThinkIB page

Regression

Pearson Correlation

Spearman’s Rank

Suggested link

Use Excel

NOTE: Google Sheets is not recommended
for IBDP statistical work

Used for determining

… whether there is a relationship between two variables.

… how strong the linear relationship is between two variables.

… how strong the non-linear monotonic relationship is between two ranked variables.

Variables

Two continuous variables.

Technically, there is no distinction between dependent and independent variables...
but common sense says one drives the other (and that the inverse is not true).

Example

How does clover leaf size vary by altitude?

How does the abundance of vegetation change with distance from the seashore in Location A?

How does the pH of HCl (pH 3, 4, 5, 6 & 7) affect the mass of a broad-ribbed Cardita shell over 12 days of immersion?

Notes

Data should be continuous.

Relationship could be linear, exponential or a polynomial.

NOTE: Sketch a scatter graph first. Relationship should be linear with no major outliers.
If these conditions are not met, then move onto a Spearman’s Rank Test.

Hypotheses

No hypotheses as not a statistical “test” per se

H₀:  There is no (linear) relationship between the two variables in the population.

H₁:  There is a (linear) relationship between the two variables in the population.

H₀:  There is no (monotonic) relationship between the two variables in the population.

H₁:  There is a (monotonic) relationship between the two variables in the population.

Interpretation

0 - 0.3 = “weak”  |  0.3 - 0.6 = “moderate”  |  0.6+ = “strong”

Link to ThinkIB page

Chi-square Test for Independence

Chi-square Goodness
of Fit Test

Suggested link

Used for determining

… whether two variables in a contingency table are independent.

… whether categorical data “fits” a hypothetical distribution. 

Variables

Two categorical variables with counts 
(discrete data).

One categorical variable.

Example

Does the abundance of Caddis flies vary between riffles and pools in XXX river?

How do the types of recycled waste in your area compare to the national average?

Hypotheses

H₀:  __ & __ are independent

H₁:  __ & __ are not independent

H₀:  data fits the description (e.g., die is fair, uniform/normal distribution, etc.)

H₁:  data does not fit the required description (e.g., die is biased, not a uniform/normal distribution…)

Interpreting the results

If the calculated p-value < 0.05, reject H₀.

Link to ThinkIB page

Paired t-test

Independent t-Test

ANOVA

Suggested link

For independent groups

For repeated groups

Used for determining

...whether there is a significant difference within 1 group following a repeated experiment by comparing their means before and after.

... whether there is a significant difference between 2 independent groups by comparing their means.

... whether there is a significant difference between 3 or more independent groups by comparing their means.

Variables

One continuous variable … that is measured for one group under two conditions

One continuous variable … that is measured for two independent groups

One continuous variable … that is measured for each independent group

Example

Has the number of horseshoe crabs on the beaches on Delaware Bay gone up or down between 2021 and 2022?

(NOTE: The number of crabs on each beach were counted in 2021 and 2022)

How does moss cover affect soil carbon sequestration? 

(Soil from “mossy” and “bare” areas are compared)

Do growth promoters (Brands A, B and C) speed up the time to flowering, measured by the time taken from the day of sowing to flowering of Zinnia plants?

(The 3 brands would be compared to a control sample)

Notes

Data is assumed to be approximately
normally distributed.

No significant outliers.

Data is assumed to be approximately
normally distributed.

No significant outliers.

Data is assumed to be approximately
normally distributed.

If result is significant continue on to Tukey’s Test to find out which groups are different
from each other.

Hypotheses

H₀:  μ₁ = μ₂

H₁:  inequality:

• μ₁ ≠ μ₂  (2-tailed test)
• μ₁ < μ₂  (1-tailed test)
• μ₁ > μ₂  (1-tailed test)

H₀:  μ₁ = μ₂

H₁:  inequality:

• μ₁ ≠ μ₂  (2-tailed test)
• μ₁ < μ₂  (1-tailed test)
• μ₁ > μ₂  (1-tailed test)

H₀:  μ₁ = μ₂ = μ₃ =... = μ_k

H₁: at least two means are significantly different

Link to ThinkIB page

Wilcoxon Rank Test

Mann Whitney Test

Kruskal-Wallis Test

Suggested link

Used for determining

...whether there is a significant difference between 2 groups following a repeated experiment by comparing their medians before and after.

...whether there is a significant difference between 2 independent groups by comparing their distributions.

...whether there is a significant difference between 3 or more independent groups by comparing their medians.

Variables

One variable … that is measured for one group under two conditions

One variable … that is measured for each group

One variable … that is measured for each group

Example

How do people rank their commitment to recycling before and after watching an educational video?

(People are asked about their recycling habits both before and after watching a video. NOTE: The same people are questioned twice).

How do two groups rank their commitment to recycling – one watches an educational video and the other does not?

Does the median number of orchids found in four different meadows vary significantly?

Notes

Aim to have more than 5 data points for each group.

Hypotheses

H₀:  median₁ = median₂

H₁:  median₁ ≠ median₂  
       (2-tailed test)

H₀:  The distribution of the first group is equal to the distribution of the second group

H₁:  The distribution of the first group is not equal to the distribution of the second group

H₀:  The medians of the groups are equal

H₁:  At least one of the medians is different from the others

Interpreting the results

If the calculated p-value < 0.05, reject H₀.