Difference between revisions of "ANLY482 AY2016-17 T2 Group10 Analysis & Findings: Analysis"

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[[ANLY482_AY2016-17_T2_Group10_Analysis_&_Findings:_Analysis|<font color="#3c3c3c"><strong>Analysis</strong></font>]]
 
[[ANLY482_AY2016-17_T2_Group10_Analysis_&_Findings:_Analysis|<font color="#3c3c3c"><strong>Analysis</strong></font>]]
 
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[[ANLY482_AY2016-17_T2_Group10_Analysis_&_Findings:_Implications|<font color="#3c3c3c"><strong>Implications</strong></font>]]
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[[ANLY482_AY2016-17_T2_Group10_Analysis_&_Findings:_Recommendations|<font color="#3c3c3c"><strong>Recommendations</strong></font>]]
 
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<!-- Body -->
 
<!-- Body -->
==<div style="background: #ffffff; padding: 17px;padding:0.3em; letter-spacing:0.1em; line-height: 0.1em;  text-indent: 10px; font-size:17px; text-transform:uppercase; font-weight: light; font-family: 'Century Gothic';  border-left:8px solid #1b96fe"><font color= #000000><strong>ACTUAL METHOD: Analysis of Variance (ANOVA) using Fit Y by X</strong></font></div>==
+
==<div style="background: #ffffff; padding: 17px;padding:0.3em; letter-spacing:0.1em; line-height: 0.1em;  text-indent: 10px; font-size:17px; text-transform:uppercase; font-weight: light; font-family: 'Century Gothic';  border-left:8px solid #1b96fe; margin-bottom:5px"><font color= #000000><strong>Analysis</strong></font></div>==
 +
 
 +
===<div style="background: #1b96fe;padding:0.6em; letter-spacing:0.1em; line-height: 0.7em; border-radius:20px; font-size:15px; text-transform:uppercase; font-weight: light; font-family: 'Century Gothic';  border-left:8px solid #1b96fe; display: inline-block; margin-bottom:10px"><font color= #fff><strong>By Therapy Group</strong></font></div>===
 +
<div style="margin:0px; padding: 10px; background: #f2f4f4; font-family: Century Gothic, Open Sans, Arial, sans-serif; border-radius: 7px; text-align:left; font-size: 15px">
 +
<b>Therapy Group 1: Adult Vaccines</b>
 +
<br/>
 +
[[File:Mattfig17.png|600px]]
 +
<br/>
 +
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.
 +
<br/>
 +
<br/>
 +
 
 +
<b>Therapy Group 2: Dermatology</b>
 +
<br/>
 +
[[File:Mattfig18.png|600px]]
 +
<br/>
 +
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.
 +
<br/>
 +
<br/>
 +
 
 +
<b>Therapy Group 3: Allergy</b>
 +
<br/>
 +
[[File:Mattfig19.png|600px]]
 +
<br/>
 +
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.
 +
<br/>
 +
<br/>
 +
 
 +
<b>Therapy Group 4: Pediatrics Vaccines</b>
 +
<br/>
 +
[[File:Mattfig20.png|600px]]
 +
<br/>
 +
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.
 +
<br/>
 +
<br/>
 +
 
 +
<b>Therapy Group 5: Urology</b>
 +
<br/>
 +
[[File:Mattfig21.png|600px]]
 +
<br/>
 +
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.
 +
<br/>
 +
<br/>
 +
 
 +
<b>Therapy Group 6: Respiratory</b>
 +
<br/>
 +
[[File:Mattfig22.png|600px]]
 +
<br/>
 +
Results show that across all category pairings (high-medium, high-low, low-medium), the p-value falls in the acceptable range, which means that there is not sufficient evidence for us to reject the null hypothesis that the means are the same.
 +
<br/>
 +
<br/>
 +
 
 +
<b>Discussion for ANALYSIS: BY THERAPY GROUP</b>
 +
<br/>
 +
Across most therapy groups (5/6), apart from respiratory, it seems that the change from low to high interactions and low to medium interactions bears positive and significant impact on the difference in means, which means that it is always better to perform high level interactions for each therapy group than low and medium level interactions. The change in means reflected is highest on the Urology group. The Respiratory group is an exception, with all p values falling in levels that deny us the chance of rejecting the null hypothesis that the means are the same.
 +
</div>
 +
 
 +
===<div style="background: #1b96fe;padding:0.6em; letter-spacing:0.1em; line-height: 0.7em; border-radius:20px; font-size:15px; text-transform:uppercase; font-weight: light; font-family: 'Century Gothic';  border-left:8px solid #1b96fe; display: inline-block; margin-bottom:10px"><font color= #fff><strong>By Sales Channel</strong></font></div>===
 
<div style="margin:0px; padding: 10px; background: #f2f4f4; font-family: Century Gothic, Open Sans, Arial, sans-serif; border-radius: 7px; text-align:left; font-size: 15px">
 
<div style="margin:0px; padding: 10px; background: #f2f4f4; font-family: Century Gothic, Open Sans, Arial, sans-serif; border-radius: 7px; text-align:left; font-size: 15px">
Analysis of Variance is a statistical method used to analyze differences among group means and  their  variances  among and between  groups. It  is also  a  form  of  statistical  hypothesis testing to test whether differences between pairs of group means are significant or not.  
+
<b>Sales Channel 1: Pharmacies</b>
<br/><br/>
+
<br/>
Prior  to  using  ANOVA,  we  have  attempted  using  linear  regression  to  generalize  the relationship  between number  of  interactions  and sales  revenue. However,  low R-squared values that suggest weak correlation and model not fitting the data were obtained, and these prompted us to carry out similar analysis using nonparametric tests like ANOVA.
+
[[File:Mattfig23.png|600px]]
<br/><br/>
+
<br/>
The primary step to carry out ANOVA is to discretize our explanatory variable - “interaction count”  into  bins  and  as such,  converting  it  from  a  numerical  to categorical  variableThe objective of discretization is because we wish to understand  whether  each  of  these interaction bins have significant differences between one another when it comes to sales revenue  (response)To define the range of interaction counts for “Low”, “Medium” and “High” interaction bins, we consulted our sponsor, who proposed that “Low” is for interaction count less than or equal to 1, “Medium” is for interaction count from 2 to 4 and “High” is for interaction count 5 and above.  
+
Results show that across all category pairings (medium-low, high-low, medium-high), the p-value falls in the acceptable range, which means that there is not sufficient evidence for us to reject the null hypothesis that the means are the same.  
 +
<br/>
 +
<br/>
 +
 
 +
<b>Sales Channel 2: Private Hospitals</b>
 +
<br/>
 +
[[File:Mattfig24.png|600px]]
 +
<br/>
 +
Results show that the p-value between the high-low category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low and high-medium category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different
 +
<br/>
 +
<br/>
 +
 
 +
<b>Sales Channel 3: Restructured Hospitals</b>
 +
<br/>
 +
[[File:Mattfig25.png|600px]]
 +
<br/>
 +
Results show that across all category pairings (high-low, high-medium, medium-low), the p-value falls in the acceptable range, which means that there is not sufficient evidence for us to reject the null hypothesis that the means are the same.  
 +
<br/>
 +
<br/>
 +
 
 +
<b>Sales Channel 4: Polyclinics</b>
 +
<br/>
 +
[[File:Mattfig26.png|600px]]
 +
<br/>
 +
Results show that the p-value between the high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the low-medium and high-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different
 +
<br/>
 +
<br/>
 +
 
 +
<b>Sales Channel 5: Specialists (Neighborhood clinics)</b>
 +
<br/>
 +
[[File:Mattfig27.png|600px]]
 +
<br/>
 +
Results show that the p-value between the all pairings(high-low, high-medium, medium-low) is way lower than 0.05 and thus we reject the null hypothesis that the means are the same.  
 +
<br/>
 +
<br/>
 +
 
 +
<b>Sales Channel 6: General Practitioner (Neighborhood clinics)</b>
 +
<br/>
 +
[[File:Mattfig28.png|600px]]
 +
<br/>
 +
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.
 +
<br/>
 +
<br/>
 +
 
 +
<b>Discussion for ANALYSIS: BY SALES CHANNEL</b>
 +
<br/>
 +
A few findings can be seen from these results:
 +
# Sales interactions increases results in significant improvement in means for neighbourhood clinics, both Specialists and General Practitioners.
 +
# Restructured hospitals and Pharmacies have not been proven to be affected by any change in interaction.
 +
# Different sales channels have extremely different patterns of sales (i.e. affected by interactions in different ways
 +
# Private hospitals only see a change in revenues when interactions are increased greatly from low to high, but not from a low to medium level.
 +
# Polyclinics behave the most oddly, with changing of interactions from medium to high having a significant improvement in mean yet there is no conclusive evidence that a change from low to medium interactions result in a change in mean revenues.
 
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<!-- Body -->
 
<!-- Body -->
==<div style="background: #ffffff; padding: 17px;padding:0.3em; letter-spacing:0.1em; line-height: 0.1em;  text-indent: 10px; font-size:17px; text-transform:uppercase; font-weight: light; font-family: "><font color= #000000><strong>Analysis</strong></font></div>==
+
==<div style="background: #ffffff; padding: 17px;padding:0.3em; letter-spacing:0.1em; line-height: 0.1em;  text-indent: 10px; font-size:17px; text-transform:uppercase; font-weight: light; font-family: 'Century Gothic';  border-left:8px solid #1b96fe; margin-bottom:5px"><font color= #000000><strong>Further Analysis, Quarter Anomalies</strong></font></div>==
 +
<div style="margin:0px; padding: 10px; background: #f2f4f4; font-family: Century Gothic, Open Sans, Arial, sans-serif; border-radius: 7px; text-align:left; font-size: 15px">
 +
For each therapy group, the team has decided to explore deeper by looking at each therapy group by quarterly performance and each sales channel by a quarterly view. We expect quarters to follow the results as in the year’s results, which otherwise, could mean that there is a certain action causing an anomaly during the quarter.
 +
<br/>
 +
<br/>
 +
 
 +
<b>Therapy Group 1: Adult Vaccines</b>
 +
<br/>
 +
[[File:Mattfig29.png|600px]]
 +
<br/>
 +
Q1, 2 and 3 of the Adult Vaccines Therapy Group follow the same result as in above. Q4 however, shows an anomaly. Results show that the p-value for the medium-low category now has a p value higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.
 +
<br/>
 +
<br/>
 +
 
 +
<b>Therapy Group 2: Dermatology</b>
 +
<br/>
 +
[[File:Mattfig30.png|600px]]
 +
<br/>
 +
Q2, 3 and 4 of the Dermatology Therapy Group follow the same result as in above. Q1 however, shows an anomaly. Q1, as in above, have inflated p-values in all categories, which means that we can no longer reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.
 +
<br/>
 +
<br/>
 +
 
 +
<b>Therapy Group 3: Allergy</b>
 +
<br/>
 +
[[File:Mattfig31.png|600px]]
 +
<br/>
 +
Q1 shows a deviation in the results where p-value for the first two pairings(high-low, medium low) now have inflated p-values, which means that we can no longer reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.
 +
<br/><br/>
 +
[[File:Mattfig32.png|600px]]
 +
<br/>
 +
Q1 shows a deviation in the results where p-value for the first pairing(high-low) now have inflated p-values, which means that we can no longer reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.
 +
<br/><br/>
 +
[[File:Mattfig33.png|600px]]
 +
<br/>
 +
Q4 shows a deviation in the results where p-value for the first two pairings(high-medium, low-medium) now have inflated p-values, which means that we can no longer reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.
 +
<br/><br/>
 +
 
 +
<b>Therapy Group 4: Pediatrics Vaccines</b>
 +
<br/>
 +
There is no deviation from the original yearly results for paediatrics vaccines
 +
<br/>
 +
<br/>
 +
 
 +
<b>Therapy Group 5: Urology</b>
 +
<br/>
 +
There is no deviation from the original yearly results for paediatrics vaccines
 +
<br/>
 +
<br/>
 +
 
 +
<b>Therapy Group 6: Respiratory</b>
 +
<br/>
 +
[[File:Mattfig34.png|600px]]
 +
<br/>
 +
Q1, 2 and 4 of the Dermatology Therapy Group follow the same result as in above. Q3 however, shows an anomaly. We can now reject the null hypothesis that the means are the same for the high-low pairing, therefore we can infer that the means are different with a change in level of interactions.
 +
<br/>
 +
<br/>
  
===<div style="background: #1b96fe;padding:0.6em; letter-spacing:0.1em; line-height: 0.7em; border-radius:20px; font-size:15px; text-transform:uppercase; font-weight: light; font-family: 'Century Gothic';  border-left:8px solid #1b96fe; display: inline-block; margin-bottom:10px"><font color= #fff><strong>BY THERAPY GROUP</strong></font></div>===
+
<b>Discussion for Further Analysis, Quarter Anomalies</b>
<div style="margin:0px; padding: 10px; background: #f2f4f4; font-family: Century Gothic, Open Sans, Arial, sans-serif; border-radius: 7px; text-align:left; font-size: 15px">
+
<br/>
 +
Most results follow the original (as in on a yearly view above) with a few exceptions. In the case of adult vaccines, while Q4 shows a higher p-value in the 2nd group, it is not extremely inflated, thus there might still actually be a change in means, making the slight exception negligible. For the case of Dermatology, there needs to be investigation done regarding Q1 as to why there is such a huge deviation in results. Oddly enough, for the allergy group, three quarters differ from the original results, which means that investigation is needed for this area too. Finally, for respiratory, there is oddly enough a category with a p-value of less than 0.05 in the first category and thus more investigation needs to be done in this area.
 
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Latest revision as of 14:03, 21 April 2017

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<< ANLY482 AY2016-17 T2 Projects


Analysis

By Therapy Group

Therapy Group 1: Adult Vaccines
Mattfig17.png
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.

Therapy Group 2: Dermatology
Mattfig18.png
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.

Therapy Group 3: Allergy
Mattfig19.png
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.

Therapy Group 4: Pediatrics Vaccines
Mattfig20.png
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.

Therapy Group 5: Urology
Mattfig21.png
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.

Therapy Group 6: Respiratory
Mattfig22.png
Results show that across all category pairings (high-medium, high-low, low-medium), the p-value falls in the acceptable range, which means that there is not sufficient evidence for us to reject the null hypothesis that the means are the same.

Discussion for ANALYSIS: BY THERAPY GROUP
Across most therapy groups (5/6), apart from respiratory, it seems that the change from low to high interactions and low to medium interactions bears positive and significant impact on the difference in means, which means that it is always better to perform high level interactions for each therapy group than low and medium level interactions. The change in means reflected is highest on the Urology group. The Respiratory group is an exception, with all p values falling in levels that deny us the chance of rejecting the null hypothesis that the means are the same.

By Sales Channel

Sales Channel 1: Pharmacies
Mattfig23.png
Results show that across all category pairings (medium-low, high-low, medium-high), the p-value falls in the acceptable range, which means that there is not sufficient evidence for us to reject the null hypothesis that the means are the same.

Sales Channel 2: Private Hospitals
Mattfig24.png
Results show that the p-value between the high-low category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low and high-medium category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different

Sales Channel 3: Restructured Hospitals
Mattfig25.png
Results show that across all category pairings (high-low, high-medium, medium-low), the p-value falls in the acceptable range, which means that there is not sufficient evidence for us to reject the null hypothesis that the means are the same.

Sales Channel 4: Polyclinics
Mattfig26.png
Results show that the p-value between the high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the low-medium and high-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different

Sales Channel 5: Specialists (Neighborhood clinics)
Mattfig27.png
Results show that the p-value between the all pairings(high-low, high-medium, medium-low) is way lower than 0.05 and thus we reject the null hypothesis that the means are the same.

Sales Channel 6: General Practitioner (Neighborhood clinics)
Mattfig28.png
Results show that the p-value between the high-low category and high-medium category is way lower than 0.05 and thus we reject the null hypothesis that the means are the same. For the medium-low category, the p value is higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.

Discussion for ANALYSIS: BY SALES CHANNEL
A few findings can be seen from these results:

  1. Sales interactions increases results in significant improvement in means for neighbourhood clinics, both Specialists and General Practitioners.
  2. Restructured hospitals and Pharmacies have not been proven to be affected by any change in interaction.
  3. Different sales channels have extremely different patterns of sales (i.e. affected by interactions in different ways
  4. Private hospitals only see a change in revenues when interactions are increased greatly from low to high, but not from a low to medium level.
  5. Polyclinics behave the most oddly, with changing of interactions from medium to high having a significant improvement in mean yet there is no conclusive evidence that a change from low to medium interactions result in a change in mean revenues.


Further Analysis, Quarter Anomalies

For each therapy group, the team has decided to explore deeper by looking at each therapy group by quarterly performance and each sales channel by a quarterly view. We expect quarters to follow the results as in the year’s results, which otherwise, could mean that there is a certain action causing an anomaly during the quarter.

Therapy Group 1: Adult Vaccines
Mattfig29.png
Q1, 2 and 3 of the Adult Vaccines Therapy Group follow the same result as in above. Q4 however, shows an anomaly. Results show that the p-value for the medium-low category now has a p value higher than 0.05, therefore we do not reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.

Therapy Group 2: Dermatology
Mattfig30.png
Q2, 3 and 4 of the Dermatology Therapy Group follow the same result as in above. Q1 however, shows an anomaly. Q1, as in above, have inflated p-values in all categories, which means that we can no longer reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.

Therapy Group 3: Allergy
Mattfig31.png
Q1 shows a deviation in the results where p-value for the first two pairings(high-low, medium low) now have inflated p-values, which means that we can no longer reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.

Mattfig32.png
Q1 shows a deviation in the results where p-value for the first pairing(high-low) now have inflated p-values, which means that we can no longer reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.

Mattfig33.png
Q4 shows a deviation in the results where p-value for the first two pairings(high-medium, low-medium) now have inflated p-values, which means that we can no longer reject the null hypothesis that the means are the same as there is not enough evidence to show that the means are different.

Therapy Group 4: Pediatrics Vaccines
There is no deviation from the original yearly results for paediatrics vaccines

Therapy Group 5: Urology
There is no deviation from the original yearly results for paediatrics vaccines

Therapy Group 6: Respiratory
Mattfig34.png
Q1, 2 and 4 of the Dermatology Therapy Group follow the same result as in above. Q3 however, shows an anomaly. We can now reject the null hypothesis that the means are the same for the high-low pairing, therefore we can infer that the means are different with a change in level of interactions.

Discussion for Further Analysis, Quarter Anomalies
Most results follow the original (as in on a yearly view above) with a few exceptions. In the case of adult vaccines, while Q4 shows a higher p-value in the 2nd group, it is not extremely inflated, thus there might still actually be a change in means, making the slight exception negligible. For the case of Dermatology, there needs to be investigation done regarding Q1 as to why there is such a huge deviation in results. Oddly enough, for the allergy group, three quarters differ from the original results, which means that investigation is needed for this area too. Finally, for respiratory, there is oddly enough a category with a p-value of less than 0.05 in the first category and thus more investigation needs to be done in this area.