# Geography Fieldwork

A Level

# Data analysis

## 4. Data analysis

Sophisticated data analysis will help you spot patterns, trends and relationships in your results. Data analysis can be qualitative and/or quantitative, and may include statistical tests. An example of a statistical test is outlined below.

## 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 geographer was interested in whether there was a difference in cliff gradient between places with a beach and places with no beach. Here are the results.

Cliff gradient where there is no beach (°) | Cliff gradient where there is a beach (°) |
---|---|

20 | 15 |

35 | 21 |

32 | 36 |

16 | 12 |

41 | 10 |

23 | 18 |

### Step 1. State the null hypothesis

There is no significant difference in cliff gradient between places with a beach and places with no beach.

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

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

No beach | Beach | ||
---|---|---|---|

Cliff gradient (°) | Rank | Cliff gradient (°) | Rank |

20 | 6 | 15 | 3 |

35 | 10 | 21 | 7 |

32 | 9 | 36 | 11 |

16 | 4 | 12 | 2 |

41 | 12 | 10 | 1 |

23 | 8 | 18 | 5 |

TOTAL | 49 | TOTAL | 29 |

(b) Calculate `∑R_1`and `∑R_2`

`∑R_1` is the sum of the ranks in the first column (no beach) = `49`

`∑R_2` is the sum of the ranks in the first column (beach) = `29`

`n_1 = 6` and `n_2 = 6`

(c) Calculate `U_1` and `U_2`

`U_1 = 6 xx 6 + 0.5 xx 6 (6 + 1) - 29 = 28`

`U_2 = 6 xx 6 + 0.5 xx 6 (6 + 1) - 49 = 8`

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

In this example, `U_1 = 28` and `U_2 = 8`

`U` is the smaller of the two values, so `U=8`

The critical value at `p=0.05` significance level for `n_1=6` and `n_2=6` is `5`. Since our calculated value of `8<6` the null hypothesis is not rejected.

In conclusion, there is no significant difference in cliff gradient between places with a beach and places with no beach.