Statistics in Geography<br />Chi squared Test<br />
When to use<br /><ul><li>Used when the aim is to observe differences between comparable sets of data.
Data needs to be collected so that it can be grouped into classes.
A null hypothesis has to be put forward, which is usually that there is no pattern to the data, or that it is distributed randomly.
The value for chi squared is then compared to significance tables, and these will confirm whether any deviation from random in the observed data is by chance or is statistically significant.</li></li></ul><li>Corrie Orientation<br />We will use an example of corrie or cirque orientation.<br />Corries were identified from maps and the direction they face was recorded. <br />Data was placed into 4 categories, relating to the compass. Results shown below<br />
Corrie Orientation<br />Is this distribution random, or significant ?<br />Start by developing null hypothesis: The orientation of corries is random.<br />If this was correct, we would expect there to be how many corries in each category ?<br />Expected E = 52 / 4 = 13 in each.<br />This is obviously not the case, but the test will determine whether the differences are significant.<br />Total number is 52.<br />
Formula<br />Formula is below:<br />X2 = Sum of (O-E)2 / E<br />O = observed frequency E = expected frequency<br />Corrie Data is set out as in table below. <br />No O or E value should fall below 5.<br />
Need to determine what are called the degrees of freedom.
This relates to the size of the sample, and is n-1 = 3.
For 3 d.o.f, value is 7.82 at the 5% significance level.</li></li></ul><li>The Answer<br /><ul><li>Since our value is greater than the value on the table we can rejectthe null hypothesis: </li></ul>eg 31.23 > table= 7.82<br /><ul><li>there is less than 1% chance of the corrie orientation being random: