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1,513 bytes added ,  11:17, 28 December 2020
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==== Per 100 ml ====
 
==== Per 100 ml ====
Defining this group of products is more difficult. We have only the fat percentage itself as indication. As the fat percentage can not be larger than 100%, we can use the specific gravity (91.1%) as limit. This assumes all oils have the same specific gravity.
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Defining this group of products is more difficult. We only have the fat percentage itself to go on. Assuming a fat percentage of 100% and a specific gravity of 0.911, the listed fat percentage should be lower than 91.1 gram (per 100g) for products that have a nutritional table per 100 ml.
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Looking at some products, the canonical rounded value is 91%, but higher values are seen as well. So we could take a limit 92%. This results in 1475 products.  
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Looking at some products, the canonical rounded value is 91g, but higher values are seen as well. So we could take a limit 92%. This will result in 1475 products.  
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This will lead to some false postives. So it is better to remove first the US-products and then extract these groups.
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There will be an overlap with the products with a US-stye nutritional table, so it is better to subtract these US-products first.
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==== Summary ====
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This grouping procedure results in group sizes of:
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* per 100g : 94 products
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* per 100ml: 2235 products
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* per vol. serving: 636 products
    
=== Calculations ===
 
=== Calculations ===
In order to get correct values, the data has been exported in CSV-format. Imported in Numbers, pruned (all non-relevant data removed), scaled by the normalisation factors, merged into one table, and finally plotted and averaged.
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In order to normalise the data, it has been exported in XLSX-format. Imported in Numbers, pruned (all non-relevant data removed), scaled by the normalisation factors, merged into one table, and finally plotted and averaged.
 
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Only the specific gravity needed to be adapted in order to get only a few fat percentages below 100%
      
=== Results ===
 
=== Results ===
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==== Grouping results ====
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For making the three groups
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This resulted in group sizes of:
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* for 100g : 94 products
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* for 100ml: 235 products
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* for serving: 636 products
      
==== Distributions ====
 
==== Distributions ====
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===== Fat =====
 
===== Fat =====
[[File:OliveOilsFatNormalisedDistribtion20201217.png|thumb|center|Distribution of normalised fat percentage (17-dec-2020)]]
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[[File:OliveOilsFatNormalisedDistribution20201224.png|thumb|center|Normalised fat percentage distribution (24-dec-2020)]]
The normalisation has worked well. All three distributions have their maximum at 100%. The largest group of 100ml has a tail below the 100%. This might be due to filtration or different specific gravities. I need to redo the graph: the x-axis label is wrong.
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If we use the standard formulas, we get quite some olive oils with a fat percentage larger than 100%. These olive oils belong to the ''per 100ml''-group. A correction of 1% of the specific gravity, i.e. 0.920 instead of 0.911, is enough to have a maximum at 100%.
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There are quite some products below the 100% line. Lowering the specific gravity by a few promille, is sufficient to increase the fat percentage. So are these really different specific gravities?
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There is also a group of products that have a specific gravity of 101.4%. What is up with these?
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===== ° Saturated fat =====
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A closer look reveals that many of these products come from the USDA import or have 1 Tbsp serving size. So they belong to the per-serving-group, but as they lack the nutritional values that such products should have, like transfat, cholesterol, etc. So how can I recognise these? The original per serving data is not available, only the 100 ml data. This can be seen from the values that are a result of conversion, like 93.333333. This is the same fat percentage that we see in the per-serving group. Thus if a product has a fat percentage between 92.9 and 93.6, it should belong to the per serving group.
The distribution spans some 4%. Normalisation seems to have worked well.
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[[File:OliveOilsNormalisedFatDistributionThree20201226.png|thumb|center|Olive oils corrected normalised fat distribution (26-dec-2020)]]
[[File:OliveOilsSaturatedFatNormalised20201217.png|thumb|center|Distribution on normalised saturated fat percentage (17-dec-2020)]]
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The corrected normalised fat distribution is shown in the graph above. Now some 1400 products have a fat percentage of 100%. Every product that falls the 100% either have indeed less than 100% fat, or are the victim of rounding errors.
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===== Mono-unsaturated fat =====
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There still lie a few products under 98% in the per 100ml group. These products have a fat percentage of 90g per 100ml. Is this a rounding issue?
The range of mono-unsaturated fat spans some 10%. It seems there are two peaks visible in the three groups.
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[[File:OliveOilsMonosaturatedFatNormalised20201217.png|thumb|center|Distribution of normalised mono-unsaturated fat percentage (17-dec-2020)]]
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===== Energy (kcal) =====
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===== Saturated fat =====
[[File:OliveOilsEnergyKcalNormalised20201217.png|thumb|center|Distribution of normalised Energy (kcal) (17-dec-2020)]]
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The distribution spans some 4%. The corrected normalisation seems to have worked well.
The three peaks seem to indicate that there are three groups. The peak seen around 857 kcal seems a off. We would expect it to be around 900 kcal. Products in this peak belong to 100g group and the per serving group. It looks like the normalisation (which was based on the fats), did not work out well. So what happened?
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[[File:OliveOilsSaturatedFatNormalisedCorrected20201226.png|thumb|center|Corrected normalised saturated fat distribution (26-dec-2020)]]
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Th 100g-group products seem to come from the USDA import, but the data was per 100g and not per serving as you would expect for this import. So the normalisation was already done, but wrong.
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===== Mono-unsaturated fat =====
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The range of mono-unsaturated fat spans some 10% with a peak at 71.5% and at 78.5%. The two peaks are present in all four groups. No explanation occurs to me.
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The canonical energy (kcal) value per serving is 120 kcal. And the canonical energy (kcal) value for the 100g-group is 900 kcal, i.e. 7.5 times larger. Where could this 7.5 factor come from? The conversion to 100 ml plus de conversion to gram, only provides a factor of 7.14. Hence the value of 857 kcal, which we see in the distribution.
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[[File:OliveOilsMonoUnsaturatedFatDistributionNormalisedCorrected20201227.png|thumb|center|Corrected normalised mono-unsaturated fat distribution (27-dec-2020)]]
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I wonder whether this difference is due to rounding issues. The US style nutritional table likes to have a simple serving size: 1 tablespoon, which translates to 15ml. But are tablespoons in de US measured in milliliters? It says so on the packages. If we calculate the tablespoon-size from 120 and 900 kcal, we get a size of 14.63 ml, i.e. rounded 15 ml. We better use this value for normalisation.
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===== Energy (kcal) =====
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[[File:OliveOilsEnergyKcalNormalisedCorrected20201227.png|thumb|center|Corrected normalised kcal-energy distribution (27-dec-2020)]]
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The distribution shows three peaks:
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* 856 kcal combines the serving, 100g and the serving in 100ml group
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* 870 kcal
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* 895 kcal
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Or 123 kcal per 15 ml would have been more accurate.
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The corrected normalisation has well worked out for the serving group, but not at all for the 100g group. We expect that the peak at 856 is the correct one. So what should the correction factor be if we want the peaks to match?
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[[File:OliveOilsKcalEnergyDistributionFudged20201227.png|thumb|center|Fudged kcal-energy distribution (27-dec-2020)]]
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The peak is roughly correct with a factor 1.055 instead of the 1.01 used earlier. No idea where this comes from.
    
==== Correlations ====
 
==== Correlations ====
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| Poly-unsaturated fat (g) || 7.1 || 11.2 || 14.3
 
| Poly-unsaturated fat (g) || 7.1 || 11.2 || 14.3
 
|}
 
|}
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==== Accuracy and Variation ====
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How accurate are the listed nutritional values? And has the apparent variation any meaning?
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Many products use the canonical values as indication for their nutritional values, like 3700kJ or 900 kcal. These are probably average values. Note that the listed accuracy is one or two significant digits. This means that it is not worthwhile to add more significant digits. Normally this implies that the variation is ± 50 kcal or 50 kJ (200 kJ?). This corresponds to the spread of values seen in the graphs above.
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One can wonder about the usefulness of products that display the nutritional values with four or five significant digits. Are those values just a reflection of statistical errors, actual differences in olive oils (year, olive, region?)
    
== OFF Conclusions and thoughts ==
 
== OFF Conclusions and thoughts ==
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