Practising Data & Stats Skills - Coloured Peppers (Answers)
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This page provides answers to the activity allowing you to practice your data and statistics skills by graphing and analysing some data on the vitamin C levels in different coloured peppers.
1. Draw an appropriate graph of the raw data.
The goal is to depict your data visually so you can see what it is revealing for each coloured pepper and between colours. It is VERY hard to see this when your data is just numbers in a table.
What we really need to show is the spread of our data. You could present your data as a box-and-whisker graph. The graph below was made using an online plot maker.
This graph helps us start to understand our data − it looks like purple peppers have the lowest concentrations of vitamin C and green peppers have the highest.
This graph could be used in an IA to justify the exclusion of the orange data point that is shown in the graph above as a dot. It is an outlier according to the box-and-whisker calculations. You would still need to explain how it might have come about.
2. Explain what your graph reveals about the raw data.
We can see from the graph that it looks like purple peppers have the lowest concentrations of vitamin C and green peppers have the highest.
Yellow peppers seem to have the greatest variance in results, while purple peppers have very low variance.
There is one potential outlier in the orange pepper data. You will need to decide what to do with this.
3. Calculate the mean and standard deviation for each concentration group.
| Coloured pepper | Mean | Std Dev |
| Red | 28.9 | 0.6 |
| Orange | 29.8 | 0.7 |
| Yellow | 30.1 | 1.7 |
| Green | 31.0 | 1.3 |
| Purple | 25.6 | 0.5 |
4. This processed data can be graphed as shown below. Explain what this graph tells you about the data.
(a) The mean for green peppers is the highest (31.0) while the mean for purple peppers is the smallest (25.6).
(b) The means for orange and yellow peppers are similar.
(c) The standard deviation for yellow peppers (1.7) is the highest, while the standard deviation for purple peppers (0.5) is the smallest.
5. Describe how you would proceed from here to analyse the data further. Consider:
- What is the goal − to compare variables or find a relationship between variables?
- What is the most appropriate statistical test?
- What would be the testing hypotheses?
- Carry out the test and write up the results.
The next step would be to use appropriate statistical tests to test whether there is a significant difference between the results for the 5 different coloured peppers − we are comparing the different colours.
In this case, we could use independent T-tests to check each pairing (Is the red pepper group different to the yellow pepper group? Is the green pepper group different to the orange pepper group? etc) OR we could use ANOVA (which is the same thing as considering each pairing).
A one-way ANOVA test for independent measures would be appropriate as our data is from independent groups. This means that we have different peppers in each group.
The testing hypotheses would be:
H0 (null hypothesis): All the population means are equal (μred = μorange = μyellow = μgreen = μpurple).
H1 (alternative hypothesis): At least one population mean is different from the rest.
Our suggested online calculator for ANOVA is HERE.
Running the data through gives the following results: The p-value is < .00001. The result is significant at p < .05
Therefore we continue on to do a Tukey's HSD (honestly significant difference) procedure to check pairwise comparisons within our ANOVA data. This tells us which pairs of colours have a statistically significant difference.
This gives the results below. The results in blue are statistically significant.
We would write these results up as follows...
A one-way ANOVA was performed to compare the concentration of vitamin C in 5 different coloured peppers. A one-way ANOVA revealed that there was a statistically significant difference in concentrations (mg/g) between at least two groups, F(4,55)=46.4, p<0.00001.
This result is statistically significant as the calculated p-value is less than 5%.
Therefore, a Tukey’s HSD Test for multiple comparisons was performed and it showed that the mean concentration of vitamin C (mg/g) was significantly different between red and green peppers. In addition, the mean concentration of vitamin C (mg/g) was significantly different between purple peppers and all the other colours. There was no statistically significant difference between the other pairings. The results are summarised in the table below.
This analysis indicates that we can conclude that the concentration of vitamin C in 5 different coloured peppers does vary. [Now relate this back to your research question…]