Inferential Statistics describe Mean Median Range Standard deviation Dispersion Central tendency

Inferential Statistic's Compare Two or more sets of data

Inferential Statistic's Associate Are two independent variable significantly related?

Correlation Test A Correlation test measures the strength of a relationship between two or more independent variables. Two examples of this type of test are a Spearman Rank Correlation Test and a Pearson Test

Correlation Test (Spearman) A Spearman Correlation test: measures the strength of a relationship between two independent variables by ranking them and then performing some simple calculations

When calculating A Spearman All calculation are rounded to two decimal places. Do not deviate from the wording and method demonstrated.

Correlation Test (spearman) A correlation test has 5 components Null Hypothesis Rationale Table of data Calculations Conclusions

Correlation Test (spearman) Null Hypothesis Ho= There is no significant relationship between how much a government invests in its military and the amount of death a country experiences Notice there is no statistical jargon included in the null hypothesis

Correlation Test (spearman) Rationale Countries that invest a lot of money in a military are often countries that do so out of need. Specifically, they are engaged in an armed conflict. Therefore the money is spent with the intention weapons will be used immediately against an enemy which is also armed. Obviously more people will then die.

Correlation Test (spearman) Rationale The more a government spends on its military, the less it has to invest in other areas that would effect the physical well being of its population. For example less money can be directed towards building and staffing hospitals. This would result in more people not being able to get required immediate medical attention when faced with a life threatening medical condition, and therefore more people would die.

Correlation Test (spearman) Table of Data Table 1: Spearman Rank Correlation Test Variables Country Death Rate (deaths/1000) Military Spending (% of GDP) Rx Ry d d2 Afghanistan 14.60 1.90 1 6.5 5.5 30.25 Argentina 5.70 0.80 13 14 Bhutan 8.80 1.00 8 5 25 Cameroon 8.00 1.30 10 9.5 0.5 0.25 Costa Rica 8.20 0.60 9 15 6 36 Congo 11.00 2.50 4 Eritrea 5.60 6.30 169 Germany 13.10 1.50 3 Guinea 10.80 1.10 11.5 42.25 Kazakhstan 6.60 12 Kenya 9.00 2.80 2.5 6.25 Lebanon 2.10 3.10 144 Libya 13.60 3.90 2 Malawi 6.80 11 1.5 2.25 Mali Source: "Rank Countries." World Geography and Culture Online. Facts On File, Inc. Web. 3 Apr. 2013. Σd2 = 482.50

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Correlation Test (spearman) Calculations rs = 1-   rs is the symbol for Spearman rank coefficient 1 and 6 are examples of the formula constant Σd2 is the sum of the differences squared column in the data table n is the number of pairs of data in the data set (i.e. countries)

Correlation Test (spearman) Calculations… cont. rs = 1-   rs = 1- rs = 1- 0.87 rs = 0.13

Correlation Test (spearman) Calculations… cont. But does the calculated value of 0.13 allow us to conclude the relationship between the two variables is significant? We need to compare this calculated value to the corresponding critical value that exists when comparing two independent variables containing 15 pairs of values

Correlation Test (spearman) Calculations… cont. To do this we must first calculate the degrees of freedom The mean is 159.00 ÷ 4 = 39.75 29 20 60 50 How many of the four numbers in this dataset can you change at the same time but still keep the exact same mean?...

Correlation Test (spearman) Calculations… cont. The mean is 159.00 ÷ 4 = 39.75 The answer is three. This is because any of three numbers can be changed , but then the final number has to be what it needs to be to add to 159. Therefore you have no freedom to change this number 29 20 60 50 n-1 (where n is the number of values in this dataset)

Correlation Test (spearman) Calculations… cont. This Spearman test has 15 countries in the dataset. But remember there are two sets of data So the degrees of freedom in this instance is n-2 Degrees of freedom = 13

Correlation Test (spearman) We now use a Spearman Critical Values table to see if the calculated value is significant. We are looking for the critical value where the degrees of freedom is 13 and confidence level is 95%

Correlation Test (spearman) Conclusion…cont. The calculated value is 0.13. The critical value using 15 countries with a 95% confidence level is ± 0.560. Since the calculated value is less than the critical value one can conclude no significant relationship exists between how much a government invests in its military and the amount of death that country experiences

Correlation Test (spearman) Conclusion…cont. But what if had got a calculated value of 0.62? The calculated value is 0.62. The critical value using 15 countries with a 95% confidence level is ± 0.560. Since the calculated value is greater than the critical value one can conclude a significant relationship exists between how much a government invests in its military and the frequency of deaths that country experiences. Specifically, as the amount a country invests in its military increases the frequency of deaths in that country also increases

Correlation Test (spearman) Conclusion…cont. But what if had got a calculated value of -0.62? The calculated value is -0.62. The critical value using 15 countries with a 95% confidence level is ± 0.560. Since the calculated value is greater than the critical value one can conclude a significant relationship exists between how much a government invests in its military and the frequency of death that country experiences. Specifically, as the amount a country invests in its military increases the frequency of deaths in that country decreases