Friday, 27 January 2012

Dear Upper Sixth,

As promised, the third post for our Unit 4B exam next week, the lovely Nikki Lewis has clarified the stats tests for you, and given you some examples to work through.

Please download the sheet to have a go, and there is an explanation there for each for you, but as a brief summary:

Spearmans Rank:

Explanation: Used to prove a relationship between two variables, the result is a positive or negative correlation, and this works well when there are only two variables, and for tests where you believe they will be connected.
Result: The result should always be between 1 and -1, and the closer to either end of that scale, the stronger the correlation.
Exam Answer: Make sure you comment on both the strength of the correlation and the level of significance at which it has been accepted, and state which hypothesis has been accepted.
Possible Tests: Type of employment against type of housing, type of employment against another type of employment (Do different economic groups live in the same region?), Population density against type of employment (Do those in higher managerial and professional roles live in less densely packed surroundings).

Chi Squared:

Explanation: A test used to asses if there is a statistically significant difference in distribution of frequencies across an area. This can be used to compare anything that can be expressed as a frequency, such as number of people employed in a certain category, or number of cars in a region. The test will tell you if there is a difference, but not where the difference is, or how much of a difference there is, once you have a positive result, you need to go back to the raw data to search for the difference and then explain the reason behind it.
Result: The result is the sum of all the Chi Squared values, and needs to be greater than the significance value for the degrees of freedom in your test. This is calculated by the number of columns minus one, multiplied by the number of rows minus one. Then you have to go back to the data to find the reason for the difference.
Exam Answer: If a difference has been proved, you can say that according to the result of the Chi Squared test, the positive hypothesis can be accepted, and there is a statistically significant difference between the distribution of frequencies in the given area. You should then refer to the observed frequencies in your test, and explain where the difference is, and any reasonable explanation, or explain how you would conduct further research to find the reason for the difference.
Possible Tests: Traffic observations over area affected by the new road network (pedestrians, lorries and cars over several areas), types of housing over areas, types of employment over areas.

Mann Whitney U:

Explanation: This test will tell you only if there is a significant difference in two sets of data, any data can be used, and for this test you do not need to have the same number of samples in each set of data. This means it is ideal for before and after surveys, particularly with the bridge, as you can add several more survey points to the new road network when it is complete, and still use this test.
Result: This test takes the lowest value or the two rows Mann Whitney values, and the result has to be BELOW the significance level for the number of data sets. The significance values will either be given to you, or will appear as a table such as this:

Exam Answer: The Mann Whitney U value shows that there has been a significant change, this can be seen in the data for x,y,z, and as such the new bridge is clearly reducing the congestion in Poole.
Possible Tests: If the result is accepted, then you have proved there is a significant difference, you need to asses the raw data to see if there is an increase or decrease.
Possible Tests: Traffic, change in population make up or densities before and after the bridge and redevelopment.

Stats for Blog

If you want us to mark any, email us, or leave a comment and I will get back to you!


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