Hypothesis Testing: Continuous Output vs. Attributive Input
Sometimes, in practice, we want to make sure we make the best decisions. For example, we want to choose for deliveries in the city, the fastest option between scooter and van.
We will use hypothesis testing, a method of proving beyond any logical doubt that a statement is true or not.
A number of statistical tools are used for data analysis, the application of which depends on the type of input and output data.
We issue the null hypothesis (H0): The delivery time is the same for both means of transport.
Alternative hypothesis (Ha): times are different.
After collecting the data follows the actual test which consists of the following steps:
1. Study of data normality.
Using Sigma XL, MINITAB or other software we can find out if the data is normally distributed. Using for example Histogram & Statistical Descriptive (Sigma XL), we notice that pvalue> 0.05 so the distribution is normal.
2. Analysis of the variations of the two distributions.
We use Test of equal variances and observe that the variations of delivery times do not differ significantly (pvalue> 0.05).
3. Location analysis (averages or medians, as appropriate).
We saw in (1.) that we have a normal distribution and that the variations do not differ (2.). So we can test the hypothesis for localization, using the 2 Sample T-Test. If there were more than two levels (in our case the two are the scooter and the van) we would have used One Way ANOVA.
Using 2 T-test samples, the pvalue obtained is <0.05 and thus we have sufficient evidence to state that there is a significant difference between the average delivery times with the two vehicles.
We also notice that the average time of the scooter is lower, so we can say that the average delivery times with the scooter are significantly shorter than those of the van.
So we will use the scooter!
We will use hypothesis testing, a method of proving beyond any logical doubt that a statement is true or not.
A number of statistical tools are used for data analysis, the application of which depends on the type of input and output data.
We issue the null hypothesis (H0): The delivery time is the same for both means of transport.
Alternative hypothesis (Ha): times are different.
After collecting the data follows the actual test which consists of the following steps:
1. Study of data normality.
Using Sigma XL, MINITAB or other software we can find out if the data is normally distributed. Using for example Histogram & Statistical Descriptive (Sigma XL), we notice that pvalue> 0.05 so the distribution is normal.
2. Analysis of the variations of the two distributions.
We use Test of equal variances and observe that the variations of delivery times do not differ significantly (pvalue> 0.05).
3. Location analysis (averages or medians, as appropriate).
We saw in (1.) that we have a normal distribution and that the variations do not differ (2.). So we can test the hypothesis for localization, using the 2 Sample T-Test. If there were more than two levels (in our case the two are the scooter and the van) we would have used One Way ANOVA.
Using 2 T-test samples, the pvalue obtained is <0.05 and thus we have sufficient evidence to state that there is a significant difference between the average delivery times with the two vehicles.
We also notice that the average time of the scooter is lower, so we can say that the average delivery times with the scooter are significantly shorter than those of the van.
So we will use the scooter!
