The minimum shows the least value in that specific area of preference e.g. lowest price for car.
The maximum shows the highest value for that area of preference e.g. highest car price.
The above are all measures of dispersion i.e. the spread of the data.
Saunders et al 1997 believes “The central tendency usually provides some general impression of values that could be seen as common, middling or average.”
The mean is the most frequently use measure of central tendency and is described as the average that includes all data values in its calculation. As in the case it be done by adding all values together and dividing the by the number of samples. This will provide a figure that will allow for the average amount that of all replies to be seen e.g. the average car price from all responses.
Saunders et al 1997 “As well as describing the central tendency for a variable, it is important to describe how the data values dispersed around the central tendency.” The method of calculating dispersion in this case will be by standard deviation. Standard deviation is the extent to which value differ from the mean. This will show how far the data is spread. This will tell us whether preferences vary from small or large range on overall responses.
Table 1 Descriptive Statistics
Table 1 above shows:
Service – It shows that the range is large in this section at 4000.00 so opinion on this option is
Spread on what consumers prefer. Also the average service required by a consumer is
9600.00 so this is the figure that will satisfy most consumers. The standard deviation is
1535.5 which tell us the variation of preference is large. On a whole what can be seen is
that there is a spread opinion amongst consumers on preference in this area.
Price – The range is £9000 this means the value between highest and lowest preference value is
large. The mean of the values is £19100 this is the average value that a consumer would
prefer to pay for the car. The variance from the mean of the data at 95% confidence is
£2954. This shows that 95% of replies are within that figure of the mean. This figure is
quite large so it can be seen that consumer preference in this area also is varied.
MPG – It can be seen that range of the replies was 8. Although smaller figure than other areas is
still significant range if size of replies taken into account. The mean of the data is 25.7 so
this is the average consumer preference in this area. The standard deviation of this mean is
2.473 which is quite a small deviation from the mean. Thus showing that data is clumped
close together and preference of most consumers is in quite a small range.
H.Power – the range of the replies was 22. This is quite a small range. The mean of the data is 129.4 for consumer preference. The standard deviation of the data is 7.7893 which shows most data is in a very small range and consumer preference is mostly based close to mean.
The next test will be a t test instead of a z test. The first reason being there is only a small sample. Secondly a t test is doing parametric testing which this data is.
Although the author is believes that he will not find any significance by doing this test he is doing it to test this hypothesis that there is no significance on a one sample test t-test. But will be interested to look at 95% Confidence Interval.
Table 2 T-test One-Sample Test
The table confirms the belief that there is no significance in any of the four variables. But what can be seen is that the 95% Confidence intervals for Price and Service have a large spread. Where as the 95%Confidence Interval for MPG and H.Power is very small. This shows that data for Price and Service is spread over a wider range thus preference in these areas is more varied than the latter two. The data for MPG and H.Power is more concentrated thus consumer preference in these areas is more agreed upon. More consumers want roughly the same level for these two things.
The author has spent very little time defining this table as shows up very little in results.
Graph 1: Miles-Per-Gallon as a Determining Purchasing Factor
MPG
MPG
The table shows that two most popular groups are 24 (30%) and 25 (20%) accounting for 50% of the data between them. This shows that 2 groups that are very close to each other can satisfy 50% of consumers. The graph shows that data can be mapped in bell shape curve.
Graph 2: Horse-Power as a Determining Purchasing Factor
H.POWER
H.POWER
Table shows data to be spread. But two groups 120 (20%) and 135 (30%) dominate 50% of the data. But there is a gap between these two groups thus spreading the data and making it harder to predict consumer preference. The graph represents this with the curve being flatter and wider than for MPG graph.
Graph 3: Service Interval as a Determining Purchasing Factor
SERVICE
SERVICE
The table shows that there are only 3 groups of data. With 8000 (40%) and 10000 (40%) dominating the responses but the range between 3 responses is large. This would explain why graph curve is flatter. This demonstrates 80% of consumers have preference within 2 ranges.
Graph 4: Price as a Determining Purchasing Factor
PRICE
PRICE
The table shows that consumer preference is spread over a large number of options. The data is spread evenly apart from at 18000 because 30% of consumer choose this as preference point. The data has the widest spread out of any option. Thus the graph curve is quite flat and long.
- Bivariate Analysis of Data
Using the appropriate techniques I will now find out if there is a relationship between the variables. Once that has been done I will attempt to find out if one variable can predict another.
The route that will be taken is the two interval variable on the table as the author has already identified as to why the interval route is to be taken. The reason for bivariate testing is that it explores and identifies relationship between variables.
Two Interval Two Nominal
Variable Variable
Two Ordinal
Variable
1.Descriptive
2. Inferential
Correlation’s
A Correlation enables me to quantify the strength of the relationship between two variables. A perfect positive correlation is represented by the value +1. This means that the two variables are closely related and as value of one changes the other will change proportionately. Also able to get negative perfect correlation –1 so as one changes other will change negatively proportionately the correlation is best shown by diagram below out of Saunders 1997:
-1 -0.7 -0.3 0 +0.3 +0.7 +1
Perfect Strong Weak Perfect weak strong perfect
Negative Positive
Descriptive Statistics
Correlations
** Correlation is significant at the 0.01 level (2-tailed).
As can be seen from the table there are 3 strong correlation’s that exist. So a strong relationship exists amongst three sets of variables. They are listed below in rank of highest correlation first:
The list is topped with Service and MPG, which has a very strong correlation so are very closely related. The author would have expected MPG and H.Power to top the list but as can be seen it came second but has a strong correlation also. The third one is service and H.Power which are correlated by to a weaker extent. So it can be seen that consumer preference on Miles per Gallon. affects their preference on both Service and Horse Power of the car.
Regression
*
a Predictors: (Constant), H.POWER
b Dependent Variable: PRICE
Residuals Statistics
a Dependent Variable: PRICE
Paired T-Test
The hypothesis for this test is that it will show Mpg and service to have a very strong relationship.
Paired Samples Statistics
Paired Samples Correlations
Paired Samples Test
From the tables above it can be seen that none of the above pairs has a strong significance and correlation. There are strong significance held by MPG and H. Power & MPG and Service but both have a weak significance. The standard deviation variance range also shows very little that has not been discussed before. Therefore hypothesis for testing proven to be wrong as no links were found as although significance high the correlation was very low at .056.
Conclusion
To conclude the report it can be clearly identified that consumer preferences on Price and Service are very spread in range. Where as consumer preferences on MPG and Horse power are closer together enabling the company to focus roughly around the mean area as the standard deviation shows. This shows that consumers want the same thing in these areas.
The bivariate analysis showed that there is a close relationship between:
Therefore there is a close relationship between these. This correlation testing proves that they are very closely linked
But the secondary testing showed that one variable cannot directly predict the another. Even though have significant areas they are not correlated enough to sustain a link.
Bibliography & References
Bajpai, A. C. et al. (1974) Engineering Mathematics,
London: Wiley & Sons Ltd
Foster, J. J. (1993) Starting SPSS/PC+ and SPSS for Windows – A beginners guide to data analysis,
Wilmslow, United Kingdom: Wiley & Sons Ltd
Jankowicz, A.D, (1995) Business Research Projects. 2nd Edition,
Cornwall, United Kingdom: Thompson Business Press
Saunders, M. et al. (1997) Research Methods for Business Students,
Harlow, Essex: Financial Times - Prentice Hall