The given scenario involves an Australian manufacturing company which already has built a name in the fashion industry but now wants to increase the existing market share through the launch of new clothing line. In this regards, the research & development department has come up with certain proposals which may be finalized and eventually go into commercial production. In this backdrop, the company needs information about the key determinants of pricing and also the ongoing trends so as to facilitate pricing of the product lines that would be launched.
A statistical analysis of the given data regarding the pricing of products belonging to different style and their corresponding brands needs to be done using statistical techniques. On one hand the existing sample characteristics can be captured using descriptive statistics while on the other meaning inferences about the population may be drawn through inferential techniques. The focus on inferential techniques would be to determine the significance of gender, brand and style for price using hypothesis testing as the underlying tool aided by various test statistics. Further, the descriptive statistics would describe the key features of the data such as variation, central tendency and distribution.
Comment
Shape – Presence of a positive skew or skew in the right direction which makes it non symmetric and also non-normal (Hastie, Tibshirani and Friedman, 2011).
Location – The mean value is higher than median which is indicative of the presence of the extreme values on the positive side thus causing a slight distortion in the mean.
Variation – The sample deviation of the price distribution above when observed in terms of the mean value would be termed as low to moderate (Flick, 2015).
Descriptive Statistics (Zara)
Histogram (Zara)
Comment
Shape – Presence of almost zero skew makes it symmetric and also normal.
Location – The mean value and the median value are converging which implies that the outliers are not present (Hastie, Tibshirani and Friedman, 2011).
Variation – The sample deviation of the price distribution above when observed in terms of the mean value would be termed as low (Hillier, 2006).
Descriptive Statistics (Tommy Hilfiger)
Histogram (Tommy Hilfiger)
Comment
Shape – Presence of a slight negative skew or skew in the left direction which makes it non symmetric and also non-normal (Hair et. al., 2015).
Location – The mean value is lower than median which is indicative of the presence of the extreme values on the lower side thus causing a slight distortion in the mean.
Variation – The sample deviation of the price distribution above when observed in terms of the mean value would be termed as moderate to high (Flick, 2015).
Descriptive Statistics (Ralph Lauren)
Histogram (Ralph Lauren)
Comment
Shape – Presence of a positive skew or skew in the right direction which makes it non symmetric and also non-normal.
Location – The mean value is higher than median which is indicative of the presence of the extreme values on the positive side thus causing a slight distortion in the mean.
Variation – The sample deviation of the price distribution above when observed in terms of the mean value would be termed as moderate to high.
Descriptive Statistics (Style 1 – Business)
Histogram (Style 1- Business)
Comment
Shape – Presence of a positive skew or skew in the right direction which makes it non symmetric and also non-normal.
Location – The mean value is higher than median which is indicative of the presence of the extreme values on the positive side thus causing a slight distortion in the mean.
Variation – The sample deviation of the price distribution above when observed in terms of the mean value would be termed as moderate.
Description statistics (Style 2-Sports)
Histogram (Style 2-Sports)
Comment
Shape – Presence of a positive skew or skew in the right direction which makes it non symmetric and also non-normal.
Location – The mean value is higher than median which is indicative of the presence of the extreme values on the positive side thus causing a slight distortion in the mean.
Variation – The sample deviation of the price distribution above when observed in terms of the mean value would be termed as moderate.
Descriptive Statistics (Style 3 – Casual)
Histogram (Style 3 – Casual)
Comment
Shape – Presence of almost zero skew makes it symmetric and also normal.
Location – The mean value and the median value are converging which implies that the outliers are not present.
Variation – The sample deviation of the price distribution above when observed in terms of the mean value would be termed as low.
Descriptive Statistics (Zara Style)
Histogram (Zara Styles)
Business – Considering that the two measures of central tendency converge, hence the distribution apparently is normal. Besides, the distribution would be symmetry and bell shaped without any skew. Also, the various measures of variability indicate that variation seems to be low for the given data when compared with the mean (Hillier, 2006).
Sports – Considering the deviation between median and mean, it may be concluded that the distribution is non-normal. Also, a leftward skew is present which reflects on the distribution being non-symmetric. Also, the various measures of variability indicate that variation seems to be low for the given data when compared with the mean (Eriksson and Kovalainen,2015).
Casual – Considering that the two measures of central tendency converge, hence the distribution apparently is normal. Besides, the distribution would be symmetry and bell shaped without any skew. Also, the various measures of variability indicate that variation seems to be low for the given data when compared with the mean (Hair et. al., 2015).
The requisite hypotheses can be written as highlighted below
Null Hypothesis (Ho): µM = µF i.e. the average prices of male and female clothing lines do not show significant difference
Alternative Hypothesis (H1): µM ≠ µF i.e. the average prices of male and female clothing lines do show significant difference
The relevant test to be deployed would be two sample t sample for the comparison of means. Further, considering difference in distributions of the two variables, the variance has been assumed ad unequal while obtaining the following excel output.
The relevant p value for the given test comes out at 0.30.
Assuming α =0.05, it is evident that p value >α. This implies non-existence of requisite evidence for causing null hypothesis rejection. Hence, it may be fair to opine that the average prices of male and female clothing lines do not show significant difference (Flick, 2015).
In the given case also, the means need to be compared but unlike in the previous case where there were two samples, the current case includes four samples in the form of the four brands and hence t test for mean difference would not be effective here as it can be used only for a maximum of 2 samples. Hence, the relevant statistic to be deployed here is the ANOVA test (Hair et. al., 2015).
The requisite hypotheses can be written as highlighted below
Null Hypothesis (Ho): µCalvin Klein = µZara = µTommyHilfiger = µRalph Lauren
Alternate Hypothesis (H1): Atleast one means out of the four means is dissimilar
It is evident on the basis of the excel output indicated above that the relevant p value is 0.
As p value (0) < α (0.05), hence it is evident that there is existence of requisite evidence to cause rejection of null hypothesis. This leads to alternative hypothesis being accepted. As a result, it may be concluded that the average prices across the four brands display a significant difference (Eriksson and Kovalainen, 2015).
In the given case also, the means need to be compared but unlike in the previous case where there were two samples, the current case includes three samples in the form of the three styles and hence t test for mean difference would not be effective here as it can be used only for a maximum of 2 samples. Hence, the relevant statistic to be deployed here is the ANOVA test (Hillier, 2006).
The requisite hypotheses can be written as highlighted below
Null Hypothesis (Ho): µBusiness = µSports = µCasual
Alternate Hypothesis (H1): Atleast one means out of the three means is dissimilar
It is evident on the basis of the excel output indicated above that the relevant p value is 0.
As p value (0) < α (0.05), hence it is evident that there is existence of requisite evidence to cause rejection of null hypothesis. This leads to alternative hypothesis being accepted. As a result, it may be concluded that the average prices across the three styles display a significant difference (Hair et. al., 2015).
In the given task, the aim is to compare the average prices of the products belonging to various styles on offer by ZARA in order to ascertain if their claim of prices being similar across styles is indeed true or not. The relevant method would be again ANOVA due to the presence of more than 2 samples whose mean needs to be compared.
The requisite hypotheses can be written as highlighted below
Null Hypothesis (Ho): µBusiness(Z) = µSports(Z) = µCasual (Z)
Alternate Hypothesis (H1): Atleast one means out of the three means is dissimilar
It is evident on the basis of the excel output indicated above that the relevant p value is 0.
As p value (0) < α (0.05), hence it is evident that there is existence of requisite evidence to cause rejection of null hypothesis. This leads to alternative hypothesis being accepted. As a result, it may be concluded that the average prices across the three styles display a significant difference (Flick, 2015).
Recommendations/Conclusion
It may be concluded from the above analysis that the clothing lines across genders does not vary in price. But the same cannot be said about brand and also the styles for which there is statistically significant variation observed from inferential statistics. Further, all the given brands tend to adhere to this particular style difference even though they may make contrary claims. While pricing the new clothing line, the company must also observe these differences and should focus on style rather than gender being the parameter for price differentiation. Since the styles typically appeal to different segments and offer difference in qualities, the underlying prices are different with the same observed for brands.
References
Eriksson, P. and Kovalainen, A. (2015) Quantitative methods in business research. 3rd edn. London: Sage Publications.
Flick, U. (2015) Introducing research methodology: A beginner’s guide to doing a research project. 4th edn. New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials of business research methods. 2nd edn. New York: Routledge.
Hastie, T., Tibshirani, R. and Friedman, J. (2011) The Elements of Statistical Learning. 4th edn. New York: Springer Publications.
Hillier, F. (2006) Introduction to Operations Research. 6th edn. New York: McGraw Hill Publications.
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