Inferential t-statistic (Welch’s two-sample t test)
In the present study, the significant impact of COVID-19 pandemic confinement on air quality in studied locations was determined by right-tailed, Welch’s two-sample t test. The complete data set was divided into two groups, pre-confinement (A) and during confinement (B) to assess if there is a statistically significant effect of confinement on AQI. Independent random samples of sizes n1, n2 were drawn by using a random number table from both the groups and applied t test using the R-software. This inferential statistic was used to test the following hypothesis:H0: No significant difference between the means of two groups i.e., no significant effect of COVID-19 pandemic confinement on AQI (μ1 = μ2).
HA: Significant difference between the means of two groups i.e., air quality is significantly improved during COVID-19 pandemic confinement (μ1 > μ2), where μ1 and μ2 are the population means of the two groups.
From Table 2, we can observe that the t-statistic (5.91), which when compared with critical t value (1.67) at 5% level of significance (α), rejected the null hypothesis and confirmed the significant reduction in the AQI for site 1. The p value was also found to be very small, suggesting that the COVID-19 pandemic confinement reduced AQI (45%). The p value revealed it is “unlikely” that we would observe such an extreme test statistic t* in the direction of HA if the null hypothesis was true. Therefore, the initial assumption that the null hypothesis is true must be incorrect. That is, since the p value, 0.00000015, is very less than α = 0.05, we reject the null hypothesis H0 : μ1 = μ2 in favor of the alternative hypothesis HA : μ1 > μ2. However, if we lowered our willingness to make a type I error to α = 0.01 instead, the significant rejection of the null hypothesis is again observed. This is due to reduction in anthropogenic activities including fuel and coal burning, vehicular emissions, and manufacturing industries.
Table 2 Welch’s two-sample t test analysis
Site 1 Site 2 Site 3 Site 4
Sample A Sample B Sample A Sample B Sample A Sample B Sample A Sample B
Mean 241.65 134.25 159.12 65.77 144.86 57.45 75.78 63.20
Observations 36 35 36 35 36 35 36 35
Hypothesized mean difference 0 0 0 0
Degree of freedom 62 38 40 42
95% confidence interval (71.05, 143.75) (69.45, 116.99) (63.14, 111.65) (1.09, 24.05)
t-statistic 5.91 7.94 7.28 2.20
P (T ≤t) one-tail 0.00000015 0.0000000014 0.0000000074 0.03
t Critical one-tail 1.67 1.68 1.68 1.68
The same behavior can be observed from the data of Table 2 for 2nd, 3rd, and 4th studied locations where the much lowered p values exhibited the statistically significant effect of COVID-19 pandemic confinement in lowering the sample mean AQI by 58%, 60%, and 17% respectively.