Measures of central tendancy- Mean, median and mod
ADVANTAGES
Simple and easy
Mode can be used with non numerical data
Median- very large and very small numbers do not affect result
Mean- useful in making measurements more accurate
DISADVANTAGES
Cant use discontinuous data
Median and mode do not account for whole set of data
Mean is easily disorted by very large/small anomalies
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Interquartile range
Interquatile range is the spread of values around the median
Find out the LQ and the HQ and the difference is the IQR
ADVANTAGES
Not affected by the outliers
DISVANTAGES
Not all data considered
Complicated to work out
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Standard deviation
the average amount by which the values in a data set vary from the mean
Calculate the mean and minus it from X
Square each of the answers and add up total
Then divide by n and square root
Low standard deviation means little range and therefore reliable mean
ADVANTAGES
More reliable measure of dispersal as it uses all the data
DISADVANTAGES
Can be greatly affected by outliers
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Spearmans rank
Formulate a null hypothesis.
Individually rank the values of each variable. 1 = highest value.
Find the difference between the two.
Square the differences and sum the values.
Input into the formula.
ADVANTAGES
Indicates the statistical significance of a result - rules out chance.
Gives numerical value to the strength and direction of a correlation.
DISADVANTAGES
Does not show if there is a casual link
Too many tied ranks affect the validity of the test.
Subject to human error.
Only appropriate for data with 10-30 values with 2 variables that are believed to be related
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Mann Whitney U
Select null hypothesis.
Rank the data sets across the two columns. 1 = lowest value.
Treat as two seperate columns. Add ranks in first column to get your R1 value then add ranks in the second column to get your R2 value.
Input int the formula.
Choose the smaller U value of either U1 or U2.
Compare to the critical values table: less than the critical value means you should reject the null hypothesis at 95% confident. Greater than the critical value - accpet the nul.
Use:
Used to show if there is a statistical difference between two sets of data e.g. size of rocks in upper course and lower course.
Cons:
Does not explain cause and effect.
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Chi square
Identify null hypothesis - no significant difference between observed an expected.
Subtract observed frequencies from expected and square the result.
Divide this by the expected value for that group.
Compare with degrees of freedom: on the critical values chart, the degree will be one less than the total number of observed values.
ADVANTAGES
To assess the degree of difference between observed and theoretical data e.g. number of pebbles along a river.
Statistical significance of results can be tested.
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