Hypothesis Testing For Manufacturing Of Chemical And Chemical Products Industry In India, Japan, And US

Independent Sample Tests

Statistical knowledge and application is way to summarize as well as categorize data. It not only helps in drawing important conclusions but also helps in quantifying the data to a specific value. The statistical knowledge here is an insight to the process behind those numbers in a business set up (Sharp et al 2015). The data that has been collected in this case is on different companies across countries. The area that the analysis will be based on the industry that deals with manufacturing of chemicals and chemical products. This “chemical industry” had been chosen primarily because this is one category that comes in every type of product used whether it is soaps or detergents (consumer chemicals), organics or inorganic or basic chemicals (Smiley and Jackson 2016). Moreover, with growing competition worldwide, there are many companies that are entering market. The countries that had been chosen are US and Japan as developed countries and India as a developing nation.

The data had been extracted from Orbit Database from the period of 2009 to 2014. However, after deleting the necessary missing areas from 503 companies, the selected sample size that had been taken is 80 for each country and total it would be 240 companies. Further to this, the data will be examined using SPSSv24 based on the given week questions of hypothesis testing and non-parametric tests.

H₀: The population mean of net assets turnover for “manufacture of chemical and chemical products” industry is equal for India and Japan (µ_IN – µ_JP = 0)

H₁: The population mean of net assets turnover for “manufacture of chemical and chemical products” industry is different for India and Japan (µ_IN – µ_JP ≠ 0)

Table 2a) V2 (1): Independent Samples Test Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper
	Levene’s Test for Equality of Variances	t-test for Equality of Means
F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Net assets turnover 2013	Equal variances assumed	4.756	0.031	1.930	158	0.055	1.130475	0.585622	-0.026181	2.287131
Equal variances not assumed			1.930	83.421	0.057	1.130475	0.585622	-0.034216	2.295166

Statistical Decision: Accept H₀ because p-value > 0.05

Conclusion: At “Levene’s test for equality of variances”, the significant value is less than 0.05 (p<0.05), then “equal variances not assumed” will be considered as null hypothesis will be rejected for equality of variances. For, “t – test for equality of means”, the t(83.421) = 1.93, p>0.05. Hence, the population mean of net assets turnover for “manufacture of chemical and chemical products” industry is equal for India and Japan (µ_IN – µ_JP = 0) as there is no significant different at 95% level.

H₀: The population mean of net assets turnover for “manufacture of chemical and chemical products” industry is equal for Japan and US (µ_JP – µ_US = 0)

H₁: The population mean of net assets turnover for “manufacture of chemical and chemical products” industry is different for Japan and US (µ_JP – µ_US ≠ 0)

Table 2a) V2 (2): Independent Samples Test
	Levene’s Test for Equality of Variances	t-test for Equality of Means
F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Net assets turnover 2013	Equal variances assumed	1.511	0.221	0.495	158	0.621	0.063325	0.127830	-0.189151	0.315801
Equal variances not assumed			0.495	154.820	0.621	0.063325	0.127830	-0.189191	0.315841

Group 1: India and Japan

Statistical Decision: Accept H₀ because p-value > 0.05

Conclusion: For independent sample test, F statistics is taken for “Levene’s test for equality of variances”, the value is significant as p<0.05 at α=0.05 for “equal variances not assumed”. Moreover, “t – test for equality of means”, the t(158) = 0.495, p>0.05, stating that H₀ is accepted. This states that population mean of net assets turnover for “manufacture of chemical and chemical products” industry is equal for Japan and US (µ_JP – µ_US = 0).

H₀: The population mean of net assets turnover for “manufacture of chemical and chemical products” industry is equal for India and US (µ_IN – µ_US = 0)

H₁: The population mean of net assets turnover for “manufacture of chemical and chemical products” industry is different for India and US (µ_IN – µ_US ≠ 0)

Table 2a) V2 (3): Independent Samples Test
	Levene’s Test for Equality of Variances	t-test for Equality of Means
F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Net assets turnover 2013	Equal variances assumed	3.928	0.049	2.046	158	0.042	1.193800	0.583619	0.041100	2.346500
Equal variances not assumed			2.046	82.313	0.044	1.193800	0.583619	0.032863	2.354737

Statistical Decision: Reject H₀ because p-value < 0.05

Conclusion: At “Levene’s test for equality of variances”, in this case, p(0.049)<0.05, then “equal variances not assumed” will be considered as H₀ will be rejected. For, “t – test for equality of means”, the t(82.313) = 2.046, p(0.044)<0.05, stating that H₀ is rejected. Hence, the population mean of net assets turnover for “manufacture of chemical and chemical products” industry is different for India and US.

H₀: The population mean of Earning after Tax (EAT) for “manufacture of chemical and chemical products” industry is equal for India and Japan (µ_IN – µ_JP = 0)

H₁: The population mean of Earning after Tax (EAT) for “manufacture of chemical and chemical products” industry is different for India and Japan (µ_IN – µ_JP ≠ 0)

Table 2a) V3 (1): Independent Samples Test
	Levene’s Test for Equality of Variances	t-test for Equality of Means
F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Earnings after Tax th USD Year – 2013	Equal variances assumed	0.110	0.741	-1.067	158	0.288	-57755.902059	54128.791445	-164665.248948	49153.444830
Equal variances not assumed			-1.067	116.105	0.288	-57755.902059	54128.791445	-164963.774907	49451.970789

Statistical Decision: Accept H₀ because p-value >0.05

Conclusion: To start “Levene’s test for equality of variances”, p(0.741)>0.05, then null hypothesis will be accepted and “equal variances assumed” row would be considered. Secondly, at the “t – test for equality of means”, the t(158) = -1.067, p(0.288)>0.05, stating that H₀ is accepted. Hence, the population mean of Earning after Tax (EAT) for “manufacture of chemical and chemical products” industry because µ_IN – µ_JP = 0.

H₀: The population mean of Earning after Tax (EAT) for “manufacture of chemical and chemical products” industry is equal for Japan and US (µ_JP – µ_US = 0)

H₁: The population mean of Earning after Tax (EAT) for “manufacture of chemical and chemical products” industry is different for Japan and US (µ_JP – µ_US ≠ 0)

Table 2a) V3 (2): Independent Samples Test
	Levene’s Test for Equality of Variances	t-test for Equality of Means
F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Earnings after Tax th USD Year – 2013	Equal variances assumed	11.598	0.001	-2.163	158	0.032	-284470.423318	131489.753506	-544174.793112	-24766.053525
Equal variances not assumed			-2.163	84.526	0.033	-284470.423318	131489.753506	-545928.444313	-23012.402324

Statistical Decision: Reject H₀ because p-value <0.05

Conclusion: Firstly, at “Levene’s test for equality of variances”, the significant value, p(0.001)<0.05, then null hypothesis will be rejected and “equal variances not assumed” row would be considered for t-test. Secondly, at the “t – test for equality of means”, the t(84.526) = -2.163, p(0.033)<0.05, stating that H₀ is rejected. Hence, the population mean of Earning after Tax (EAT) for “manufacture of chemical and chemical products” industry is significantly statistically valid because earnings are different for Japan and US (µ_JP – µ_US ≠ 0).

Group 2: Japan and US

H₀: The population mean of Earning after Tax (EAT) for “manufacture of chemical and chemical products” industry is equal for India and US (µ_IN – µ_US = 0)

H₁: The population mean of Earning after Tax (EAT) for “manufacture of chemical and chemical products” industry is different for India and US (µ_IN – µ_US ≠ 0)

Table 2a) V3 (3): Independent Samples Test
	Levene’s Test for Equality of Variances	t-test for Equality of Means
F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Earnings after Tax th USD Year – 2013	Equal variances assumed	11.101	0.001	-2.480	158	0.014	-342226.325377	138020.151668	-614828.832812	-69623.817942
Equal variances not assumed			-2.480	100.751	0.015	-342226.325377	138020.151668	-616029.376934	-68423.273820

Conclusion: For independent sample test, F statistics is taken for “Levene’s test for equality of variances”, the value is significant as p<0.05 at α=0.05 for “equal variances not assumed”. Moreover, “t – test for equality of means”, the t(158) = -2.480, p(0.014)<0.05, stating that H₀ is rejected. This states that population mean of Earning after Tax (EAT) for “manufacture of chemical and chemical products” industry is different for India and US.

H₀: The population proportion of companies with gross margin of at least 30% is same for India and Japan (ρ_IN – ρ_JP = 0)

H₁: The population proportion of companies with gross margin of at least 30% is different for India and Japan (ρ_IN – ρ_JP ≠ 0)

Table 2a) V4 (1): Independent Samples Test
	Levene’s Test for Equality of Variances	t-test for Equality of Means
F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Gross Margin %	Equal variances assumed	34.020	0.000	3.923	158	0.000	0.28750	0.07328	0.14277	0.43223
Equal variances not assumed			3.923	153.153	0.000	0.28750	0.07328	0.14273	0.43227

Statistical Decision: Reject H₀ because p-value <0.05

Conclusion: The “Levene’s test for equality of variances” is significantly valid taking in considering that H₀ is rejected and “equal variances not assumed” is considered at 95% level. Further, t(153.153)= 3.923 is statistically valid because p is 0.00<0.05. Therefore, reject the null hypothesis because the population proportion of companies with gross margin of at least 30% is different for India and Japan.

H₀: The population proportion of companies with gross margin of at least 30% is equal for Japan and US (ρ_JP – ρ_US = 0)

H₁: The population proportion of companies with gross margin of at least 30% is different for Japan and US (ρ_JP – ρ_US ≠ 0)

	Table 2a) V4 (2): Independent Samples Test
	Levene’s Test for Equality of Variances	t-test for Equality of Means
F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Gross Margin %	Equal variances assumed	0.897	0.345	-0.873	157	0.384	-0.06946	0.07954	-0.22657	0.08764
Equal variances not assumed			-0.873	156.993	0.384	-0.06946	0.07954	-0.22656	0.08764

Statistical Decision: Accept H₀ because p-value >0.05

Conclusion: The “Levene’s test for equality of variances” is not valid and H₀ is accepted and “equal variances assumed” is considered at 95% level of significance. Further, t(158)= -0.873 is not significant because p for t-test is 0.384>0.05. Therefore, accept the null hypothesis because the population proportion of companies with gross margin of at least 30% is equal for Japan and US.

H₀: The population proportion of companies of gross margin with at least 30% is equal for India and US (ρ_IN – ρ_US = 0)

H₁: The population proportion of companies with gross margin of at least 30% is different for India and US (ρ_IN – ρ_US ≠ 0)

Table 2a) V4 (3): Independent Samples Test
	Levene’s Test for Equality of Variances	t-test for Equality of Means
F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
Lower	Upper
Gross Margin %	Equal variances assumed	29.237	0.000	2.978	157	0.003	0.21804	0.07321	0.07344	0.36263
Equal variances not assumed			2.975	151.836	0.003	0.21804	0.07329	0.07325	0.36283

Conclusion: The “Levene’s test for equality of variances” is significantly valid taking in considering that H₀ is rejected and “equal variances not assumed” is considered at 95% level. Further, t(151.836)= 3.923 is statistically valid because p for t-test is 0.003<0.05. Therefore, reject the null hypothesis because the population proportion of companies with gross margin of at least 30% is different for India and US at α=0.05.

Group 3: India and US

H₀: There is no significant difference between the population mean for net assets turnover between 2009 and 2010 for chemical and chemical products industry in US i.e. the country has not recovered the worldwide effect (µ₂₀₀₉ – µ₂₀₁₀ = 0).

H₁: There is significant difference between the population mean for net assets turnover between 2009 and 2010 for chemical and chemical products industry in US i.e. the country has recovered the worldwide effect and net assets turnover in 2010 is greater than 2009 (µ₂₀₀₉ – µ₂₀₁₀ > 0).

Table 2b) V2: Paired Samples Test
	Paired Differences	t	df	Sig. (2-tailed)
Mean	Std. Deviation	Std. Error Mean	95% Confidence Interval of the Difference
Lower	Upper
Pair 1	Net assets turnover Year – 2009_US – Net assets turnover Year – 2010_US	0.208987	0.468043	0.052659	0.104151	0.313823	3.969	78	0.000

Statistical Decision: Reject H₀ because p-value <0.05

Conclusion: At 5% level of significance, it can be seen that t(78) = 3.969 and p(0.00)<0.05 level which states that the results have been valid and significant and rejects null hypothesis. Hence, it states that there is significant difference between the population mean for net assets turnover between 2009 and 2010 because US had recovered the worldwide effect and net assets turnover in 2010 was greater than 2009 (µ₂₀₀₉ – µ₂₀₁₀ > 0).

H₀: There is no significant difference between the population mean for Earnings after Tax (EAT) between 2009 and 2010 for chemical and chemical products industry in US i.e. the country has not recovered the worldwide effect (µ₂₀₀₉ – µ₂₀₁₀ = 0).

H₁: There is significant difference between the population mean for Earnings after Tax (EAT) between 2009 and 2010 for chemical and chemical products industry in US i.e. the country has recovered the worldwide effect and EAT in 2010 is greater than 2009 (µ₂₀₀₉ – µ₂₀₁₀ > 0).

Table 2b) V3: Paired Samples Test
	Paired Differences	t	df	Sig. (2-tailed)
Mean	Std. Deviation	Std. Error Mean	95% Confidence Interval of the Difference
Lower	Upper
Pair 1	Earnings after Tax th USD Year – 2009_US – Earnings after Tax th USD Year – 2010_US	84138.508223	237841.933483	26591.536558	31209.378690	137067.637756	3.164	79	0.002

Conclusion: At 5% level of significance, it can be seen that t(79) = 3.164 and p(0.002)<0.05 level which states that the results have been valid and significant and rejects null hypothesis. Hence, it states that there is significant difference between the population mean for Earnings after Tax (EAT) between 2009 and 2010 because US had recovered the worldwide effect and earnings after tax in 2010 was greater than 2009 (µ₂₀₀₉ – µ₂₀₁₀ > 0).

H₀: The differences of two population distribution (India – Japan) on net assets turnover for “chemical and chemical products” are identical.

H₁: The differences of two population distribution (India – Japan) on net assets turnover for “chemical and chemical products” are not identical.

Table 3a) V2 (1): Hypothesis Test

Statistical Decision: Reject H₀ because p-value <0.05

Conclusion: At 5% level of significance, the evidence does not support null hypothesis because p=0.001. Hence, it states that the differences of two population distribution (India – Japan) on net assets turnover for “chemical and chemical products” are not identical.

V3: Earnings after Tax (EAT)

H₀: The differences of two population distribution (Japan – US) on net assets turnover for “chemical and chemical products” are identical.

H₁: The differences of two population distribution (Japan – US) on net assets turnover for “chemical and chemical products” are not identical.

Table 3a) V2 (2): Hypothesis Test

Statistical Decision: Accept H₀ because p-value >0.05

Conclusion: At 5% level of significance, the evidence does accepts null hypothesis because p=0.313 which is higher than p=0.05. Hence, it states differences of two population distribution (Japan – US) on net assets turnover for “chemical and chemical products” are identical.

H₀: The differences of two population distribution (India – US) on net assets turnover for “chemical and chemical products” are identical.

H₁: The differences of two population distribution (India – US) on net assets turnover for “chemical and chemical products” are not identical.

Table 3a) V2 (3): Hypothesis Test

Statistical Decision: Reject H₀ because p-value <0.05

Conclusion: At 5% level of significance, the null hypothesis cannot be accepted because p=0.000 which is lesser than p=0.05. Hence, it states that the differences of two population distribution (India – US) on net assets turnover for “chemical and chemical products” are not identical.

èNon parametric test is a better test in this case because the computation of an independent sample t tests is much complicated than a non parametric tests (Corder and Foreman 2014). Also, there are fewer assumptions to be catered to. Moreover, it is irrespective of the data being normally distributed or not.

H₀: The differences of two population distribution (India – Japan) of Earnings after Tax (EAT) for “chemical and chemical products” are identical.

H₁: The differences of two population distribution (India – Japan) of Earnings after Tax (EAT) for “chemical and chemical products” are not identical.

Table 3a) V3 (1): Hypothesis Test

Statistical Decision: Reject H₀ because p-value <0.05

Conclusion: At 5% level of significance, the null hypothesis cannot be accepted because p=0.000 which is lesser than p=0.05. Hence, it states that the differences of two population distribution (India – Japan) of Earnings after Tax (EAT) for “chemical and chemical products” are not identical.

H₀: The differences of two population distribution (Japan – US) of Earnings after Tax (EAT) for “chemical and chemical products” are identical.

H₁: The differences of two population distribution (Japan – US) of Earnings after Tax (EAT) for “chemical and chemical products” are not identical.

Table 3a) V3 (2): Hypothesis Test

Statistical Decision: Accept H₀ because p-value >0.05

Group 1: India and Japan

Conclusion: At 5% level of significance, the evidence does accepts null hypothesis because p=0.313 which is higher than p=0.05. Hence, it states that the differences of two population distribution (Japan – US) of Earnings after Tax (EAT) for “chemical and chemical products” are identical.

H₀: The differences of two population distribution (India – US) of Earnings after Tax (EAT) for “chemical and chemical products” are identical.

H₁: The differences of two population distribution (India – US) of Earnings after Tax (EAT) for “chemical and chemical products” are not identical.

Table 3a) V3 (3): Hypothesis Test

Statistical Decision: Reject H₀ because p-value <0.05

Conclusion: At 5% level of significance, the null hypothesis is rejected because p<0.05. Hence, it states that the differences of two population distribution (India – US) of Earnings after Tax (EAT) for “chemical and chemical products” are not identical.

èWhen analyzing EAT, non parametric test was easy to compute and come up to the result of testing of hypotheses instead of independent t test in which equality of variances is considered and later equality of means. On the contrary, these ranks are more not sensitive to the outliers present in the data and it can be both nominal and ordinal in nature (Edgington 2015).

H₀: The differences of population proportion of companies with gross margin of at least 30% are identical for India and Japan.

H₁: The differences of population proportion of companies with gross margin of at least 30% are not identical for India and Japan.

Table 3a) V4 (1): Wixcoxin rank Sum Test

Statistical Decision: Reject H₀ because p-value <0.05

Conclusion: At 5% level of significance, the null hypothesis is rejected because p<0.05. Hence, it states that differences of population proportion of companies with gross margin of at least 30% are not identical for India and Japan.

H₀: The differences of population proportion of companies with gross margin of at least 30% are identical for Japan and US.

H₁: The differences of population proportion of companies with gross margin of at least 30% are not identical for India and Japan.

Table 3a) V4 (2): Wixcoxin rank Sum Test

Statistical Decision: Accept H₀ because p-value >0.05

Conclusion: At 5% level of significance, the null hypothesis is accepted because p>0.05. Hence, it states that differences of population proportion of companies with gross margin of at least 30% are identical for Japan and US.

H₀: The differences of population proportion of companies with gross margin of at least 30% are identical for India and US.

Group 2: Japan and US

H₁: The differences of population proportion of companies with gross margin of at least 30% are not identical for India and US.

Table 3a) V4 (3): Wixcoxin rank Sum Test

Statistical Decision: Reject H₀ because p-value <0.05

Conclusion: At 5% level of significance, the null hypothesis is rejected because p<0.05. Hence, it states that differences of population proportion of companies with gross margin of at least 30% are not identical for India and US.

èAs per the results on gross margin%, non parametric tests would be considered as it helps in forming decisions soon and without homogeneity of variance. Also, are categorical in nature as in this case when gross margin at 30% or more is taken 1 and below 30% is taken as zero.

H₀: There is no difference in population distribution (2009-2010) for net assets turnover in chemical and chemical products industry in US i.e. the country has not recovered the worldwide effect.

H₁: There is difference in population distribution (2009-2010) for net assets turnover in chemical and chemical products industry in US i.e. the country has recovered from the worldwide effect.

Table 3b) V2: Wixcoxin signed rank test US

Statistical Decision: Reject H₀ because p-value <0.05

Conclusion: At α=0.05 level of significance, the wilcoxon signed rank test has shown the results to be significant because p>0.05. Hence, it states that difference in population distribution (2009-2010) for net assets turnover in chemical and chemical products industry in US has become positive in 2010 because it had recovered from worldwide effect.

èWilcoxon test has been preferred in this because the N-par tests assumption are not rigid as paired sample t –tests. The conditions of non parametric often lead to symmetrical results for differences rather than the sample being random and independent (Matsouaka, Singhal and Betensky 2016). However, if we further depict that sample size than a parametric test should be used because its normality can b viewed.

H₀: There is no difference in population distribution (2009-2010) for Earnings after Tax (EAT) in chemical and chemical products industry in US i.e. the country has not recovered the worldwide effect.

H₁: There is difference in population distribution (2009-2010) for Earnings after Tax (EAT) in chemical and chemical products industry in US i.e. the country has recovered from the worldwide effect.

Table 3b) V3: Wixcoxin signed rank test US

Statistical Decision: Reject H₀ because p-value <0.05

Conclusion: At α=0.05 level of significance, the wilcoxon signed rank test has shown the results to be significant because p is 0.001 which is less than>0.05. Hence, it states that the difference in population distribution (2009-2010) for Earnings after Tax (EAT) in chemical and chemical products industry in US has become positive in 2010 because it had recovered from worldwide effect.

èThe asymptotic results and valid results are considered without any hurdle for the use of examination of results (Edgington 2015). Hypothesis tests are enough to draw a conclusion on the study of even a large sample with direct implication on its statistical significance of earnings after tax in two different years.

References:

Corder, G.W. and Foreman, D.I., 2014. Nonparametric statistics: A step-by-step approach. John Wiley & Sons.

Edgington, E.S., 2015. Nonparametric tests for single-case experiments. In Single-Case Research Design and Analysis (Psychology Revivals) (pp. 145-170). Routledge.

Matsouaka, R.A., Singhal, A.B. and Betensky, R.A., 2016. An optimal Wilcoxon–Mann–Whitney test of mortality and a continuous outcome. Statistical methods in medical research, p.0962280216680524.

Sharpe, N.R., De Veaux, R.D., Velleman, P.F. and Wright, D., 2015. Business statistics. Pearson.

Smiley, R.A. and Jackson, H.L., 2016. Chemistry and the chemical industry: a practical guide for non-chemists. CRC press.