Using the t test to determine the statistical difference in the number of days it takes to start a business between emerging and developed markets
Learning Institution
Introduction
According to World Bank (2015), the time required to start a business is defined as the number of days needed to legally operate a business in a given jurisdiction, usually a country. This study was conducted to find out if there were statistically significant differences in the average number of days it takes to start a business between developed markets and emerging markets. Time and cost are deemed important due to the impact they may have on a company’s operations and finances. Data obtained from the world bank (World Bank, 2015) based on the year 2015 for 15 emerging and 15 developed markets was collected and analyzed using independent samples t test at 95% confidence level. It was then analyzed to determine if there were statistical differences in the time it takes to start a business in the above two markets.
The t test can also be applied in similar situations such as;
Economics: Is the economic growth of emerging markets in South America greater than the economic growth of emerging markets in Asia
Healthcare: Does the use of drug A improve the status of patients than drug B?
Finance: Does lowering interest rates improve borrowing participation in males than females and vice versa.
Our Sample
Our sample included random data selection from 15 countries from around the world
We want to compare the mean number of days to open a business in developed markets and in emerging markets. In other words, we compare two mean values. The groups are independent. Our assumptions that were met before using the independent samples t test were;
Sample data were collected at random
The dependent variable is measured on a continuous/scale (Number of days to start a business)
The data is approximately normally distributed.
There are no significant outliers in the dataset.
Homogeneity of variance was assumed (though violated in the actual analysis)
Since the normality assumption is mentioned above, we can choose a Student’s t-test for independent samples to examine the difference between the population mean values.
Our Hypotheses
Let population mean 1, µ1 be population mean of developed markets, and population mean 2 (µ2) be the population mean of emerging markets. Then, the pair of hypotheses tested are:
Null hypothesis: there is no significant difference between the population mean of developed markets and population mean of emerging markets. Alternative hypothesis: there is a significant difference between the population mean of developed markets and population mean of emerging markets. Mathematically, it could be written as follows:
Null hypothesis, H0: µ1 = µ2
Alternate hypothesis, H1: µ1 ≠ µ2
The level of significance is set at the most common level for such research works – 0.05 or 5%. Since we test the alternative hypothesis that the mean values are not equal, we have to choose a two-tailed test.
Data analysis
Using Excel (Microsoft, n.d) and (or) SPSS (IBM), the descriptive and inferential statistics such as the mean, median, variance, and standard deviation were obtained and analyzed. Descriptive statistics revealed that the average number of days it takes to start a business in a developed country was 5 days compared to 28.4 days for emerging markets.
The independent t test compares the means between two unrelated groups based on a continuous dependent variable and in our case the dependent variable was the number of days it took to open a business while the independent variable was a grouping variable - the emerging and developed countries. An independent sample t test was chosen because we do not know the population mean and standard deviation (Western Michigan University, n.d.). According to the results of the Student’s t-test, the t-observed is equal to -4.59, the corresponding p-value is 0.00036. The critical value of t-test is 1.75405, this value is less than 4.59. Thus, we reject the null hypothesis.
Results and conclusion
References
International Business Machines (2015). SPSS 20, IBM
The World Bank. (2015). The time required to start a business. Retrieved on 7 April 2016 from http://data.worldbank.org/indicator/IC.REG.DURS
Western Michigan University (n.d). Hypothesis testing. Retrieved on 7 April 2016 from http://www.stat.wmich.edu/s216/htests/htests.html
