# Biology Fieldwork

A Level

# Discussion

## 3. Discussion

## Simpson's Diversity Index

Simpson's Diversity Index is a measure both of species richness (i.e. the number of different species present) and species evenness (i.e. how evenly distributed each species is).

`D = (Nxx(N-1)) / (Σ nxx(n-1))`

- `D` = Simpson's Diversity Index
- `n` = the number of individuals of each species
- `N` = the total number of individuals

## Mann Whitney U test

Mann Whitney U is a statistical test that is used either to test whether there is a significant difference between the medians of two sets of data.

The Mann Whitney U test can only be used if there are at least 6 pairs of data. It does not require a normal distribution.

There are 3 steps to take when using the Mann Whitney U test

### Step 1. State the null hypothesis

There is no significant difference between _______ and _______

### Step 2. Calculate the Mann Whitney U statistic

`U_1= n_1 xx n_2 + 0.5 n_2 (n_2 + 1) - ∑ R_2`

`U_2 = n_1 xx n_2 + 0.5 n_1 (n_1 + 1) - ∑ R_1`

- `n_1` is the number of values of `x_1`
- `n_2` is the number of values of `x_2`
- `R_1` is the ranks given to `x_1`
- `R_2` is the ranks given to `x_2`

### Step 3. Test the significance of the result

Compare the value of U against the critical value for U at a confidence level of 95% / significance value of P = 0.05.

If U is equal to or smaller than the critical value (p=0.05) the REJECT the null hypothesis. There is a SIGNIFICANT difference between the 2 data sets.

If U is greater than the critical value, then ACCEPT the null hypothesis. There is NOT a significant difference between the 2 data sets.

### Worked example

A biologist is investigating whether there is a difference in woodland flora between two contrasting areas of woodland, Site A and Site B. Eight randomly placed frame quadrat samples in each of two contrasting areas of woodland produced the following % cover of dog's mercury, a common woodland plant. Here are the results.

Quadrat | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Site A | 26 | 14 | 8 | 6 | 26 | 20 | 11 | 13 |

Site B | 28 | 16 | 26 | 25 | 25 | 24 | 16 | 28 |

### Step 1. State the null hypothesis

There is no significant difference in species richness between Site A and Site B.

### Step 2. Calculate Mann Whitney U statistic

(a) Give each result a rank. Calculate the sum of the ranks for the two columns.

Now arrange the data values in order, and give each value a rank in order from smallest to highest

Site A | 6 | 8 | 11 | 13 | 14 | 20 | 26 | 26 |

rank | 1 | 2 | 3 | 4 | 5 | 8 | 13 | 13 |

Site B | 16 | 16 | 24 | 25 | 25 | 26 | 28 | 28 |

rank | 6.5 | 6.5 | 9 | 10.5 | 10.5 | 13 | 15.5 | 15.5 |

(b) Calculate `∑R_1`and `∑R_2`

`∑R_1` is the sum of the ranks in the first column (Site A) = `49`

`∑R_2` is the sum of the ranks in the first column (Site B) = `87`

`n_1 = 8` and `n_2 = 8`

(c) Calculate `U_1` and `U_2`

`U_1 = 8 xx 8 + 0.5 xx 8 xx (8 + 1) – 87 = 13`

`U_2 = 8 xx 8 + 0.5 xx 8 xx (8 + 1) – 49 = 51`

### Step 3. Test the significance of the result

In this example, `U_1 = 13` and `U_2 = 51`

`U` is the smaller of the two values, so `U=13`

The critical value at `p=0.05` significance level for `n_1=8` and `n_2=8` is `13`. Since our calculated value of `13 = 13`, the null hypothesis can be rejected.

In conclusion, there is a significant difference in species richness between Site A and Site B.