Inference Statistics

Please make sure you have merged the two datasets. Check Merging for instructions.

Hypothesis testing

From Wikipedia:

To determine whether a result is statistically significant, a researcher calculates a p-value, which is the probability of observing an effect of the same magnitude or more extreme given that the null hypothesis is true.

The null hypothesis is rejected if the p-value is less than a predetermined level, α.

α is called the significance level, and is the probability of rejecting the null hypothesis given that it is true (a type I error).

α is usually set at or below 5%.

Our null hypotheses

H01 There is no difference in the Average temperature in the gas & oil and the electronic era

Independent T-test

It is often used to see whether there is a group difference in continuous data between two groups

We can only run a T-test if our model follows certain assumptions:

  1. Independence
  2. Normality
  3. Equal variance

Input

t.test(AverageTemperature ~ era, data=carbon, var.eq=TRUE)

Output

Two Sample t-test
    
data:  AverageTemperature by era
t = 3.7437, df = 54, p-value = 0.0004415
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
    0.1806106 0.5970976
sample estimates:
mean in group electronic  mean in group gas & oil 
                19.13249                 18.74364

Interpreting the results:

  • t value guides our analysis. Read more at this link
  • df = 54 degrees of freedom

  • p-value < 0.0004415 is smaller than α = 0.05 so that means that we can reject the null hypothesis

  • Which one seems higher?
    • mean in group gas & oil = 18.74364
    • mean in group eletronics = 19.13249



Correlation

H02 Is there any association between the AverageTemperature and the AverageCarbonEmission ?

Pearson’s correlation

Is used to examine associations between variables (represented by continuous data) by looking at the direction and strength of the associations

Input

cor.test(carbon$AverageTemperature, carbon$AverageCarbonEmission, method="pearson")

Output

    
Pearson's product-moment correlation

data:  carbon$AverageTemperature and carbon$AverageCarbonEmission
t = 14.919, df = 54, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
    0.8299122 0.9386169
sample estimates:
        cor 
0.8970832

Interpreting the results:

  • p-value < 2.2e-16 so that means that there is statistically significant correlation between temperature and carbon emission

  • How strong is the correlation cor = 0.8970832

  • Interpretation varies by research field so results should be interpreted with caution

  • cor varies from -1 to 1 positive values indicate that an increase in the x variable increases the y variable. In this case, a value closer to 1 means a strong positive correlation

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