20120920 - Nutritional balance of potato chips (inferential statistics) - 2012

[Data] (Note: A revised version of this article exists6)
[<Normal page] [PEREZGONZALEZ Jose D (2012). Nutritional balance of potato chips (inferential statistics). Journal of Knowledge Advancement & Integration (ISSN 1177-4576), 2012, pages 259-263.]

BNI of potato chips (inferences)

Perezgonzalez assessed the nutritional balance of potato chips7 in 2012, as part of a research on the nutritional composition of snacks in New Zealand. This article provides inferential information about the population of products under research (foodBNI) as well as about a hypothetical diet based on those products (dietBNI).


The population of potato chips appears as highly unbalanced8 (illustration 1). Indeed, it can be inferred, with a 95% degree of confidence, that the median nutritional balance is located somewhere between BNI 79.42 and BNI 85.88, and the mean a bit higher, somewhere between BNI 83.87 and BNI 89.14, thus indicative of a tendency (skewness) for potato chips towards higher unbalance.

Illustration 1: Food's nutritional balance
Non-parametric BNI WHO US/CAN AUS/NZ UK
Median CI95 lower 79.42 79.42 67.90 67.90 67.90
Median CI95 upper 85.88 85.88 73.32 73.32 73.32
SPR lower 6.10 6.10 4.38 4.38 4.38
SPR upper 12.56 12.56 9.80 9.80 9.80
Mean CI95 lower 83.87 83.87 71.22 71.22 71.22
Mean CI95 upper 89.14 89.14 75.64 75.64 75.64
SD CI95 lower 8.63 8.63 7.23 7.23 7.23
SD CI95 upper 12.29 12.29 10.31 10.31 10.31
(95% confidence interval's lower and upper bounds)

Similar nutritional profiles appear when using other international recommended dietary intakes (RDIs), as well. Indeed, the correlation between indexes is very high or perfect between these indexes (illustration 2). These correlations would occur by chance less than one in 1000, thus it can be inferred that they truly reflect an underlying relationship between international indexes.

Illustration 2: Correlations between international RDIs
BNI (CI95 lower) 1.000 .840 .840 .840
BNI (CI95 upper) 1.000 .942 .942 .942
WHO (CI95 lower) 1.000 .840 .840 .840
WHO (CI95 upper) 1.000 .942 .942 .942
US/CAN (CI95 lower) .975 .975 1.000 1.000
US/CAN (CI95 upper) .991 .991 1.000 1.000
AUS/NZ (CI95 lower) .975 .975 1.000 1.000
AUS/NZ (CI95 upper) .991 .991 1.000 1.000
UK (CI95 lower) .975 .975 1.000 1.000
UK (CI95 upper) .991 .991 1.000 1.000
(95% confidence interval's lower and upper bounds)


As part of a hypothetical diet in which all products contributed the same weight of chips, the resulting nutritional balance would still be highly unbalanced, with 95% confidence of it ranging somewhere between BNI 66.10 and BNI 74.29 (when fiber is estimated). However, differences in international RDIs become more apparent at this level, as this diet would "benefit" more under certain international RDIs than under others. For example, it would range between 63.17 and 71.35 under WHO's RDIs, but between 43.12 and 49.96 under UK's RDIs, a rather moderate unbalance, in comparison.

Illustration 3: Diet's nutritional balance (potato chips)
CI95 Protein Carbs Sugar Fat Sat.fat Fiber Sodium
lower 5.7 51.4** 1.4 32.1 10.5 4.4* 0.581
upper 6.1 49.8** 1.8 33.0 13.2 4.4* 0.697
CI95 International RDIs BNI WHO US/CAN AUS/NZ UK
lower (diet, fiber unest.) 80.77 80.77 67.56 67.56 67.56
upper (diet, fiber unest.) 88.95 88.95 74.41 74.41 74.41
lower (diet, fiber est.*) 66.10 63.17 53.59 54.23 43.12
upper (diet, fiber est.*) 74.29 71.35 60.44 61.07 49.96
(Nutrients per 100g; *fiber content estimated from USDA database5; **carbs' upper and lower bounds are reversed9)

In any case, the most visible differences between the lower and upper bounds of this confidence interval are the levels of saturated fat and sodium that these products provide to the diet.

Illustration 4: dietBNI CI95 lower bound
60% *
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mid p c f fb
max s sf na
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ideal % = grey cells; actual % = asterisk (*)
Illustration 5: dietBNI CI95 upper bound
60% *
55% *
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35% * *
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ideal % = grey cells; actual % = asterisk (*)


Research approach

Exploratory study for inferring the nutritional balance of the population of potato chips7 in New Zealand.


Quantitative (fixed) in nature, including a mix of a descriptive design and a relational design.


Stratified sample of 63 potato chip products2, including generic and proprietary brands, diverse flavors and other relevant categories. The actual products were collected in a convenient manner from three major national supermarket chains. Notwithstanding this, the final sample covered a large proportion of the population of potato chip products available in such supermarkets. Thus, given the scope of the sample and the national coverage of the retail chains behind the supermarkets sampled, the actual sample is fairly representative of the population of potato chips available to New Zealanders nationwide. It may also partially inform about the population of potato chips available to Australians, as one of the retail chains is Australian-owned and several of the products are imported from (and others probably exported to) Australia.


Variables of interest for this research were the following:

  • Weight contribution of seven nutrients (protein, carbohydrates, sugars, fats, saturated fat, fiber and sodium) to 100g of the food product.
  • The Balanced Nutrition Index (BNI) of each food product, as calculated from above variables.
  • Aggregated information for the sample of products (foodBNI).
  • Aggregated information about the individual nutrients for the simulation of a potato-chip-based diet (dietBNI).

Materials and procedure

Relevant data were collected in person by purchasing the food products or by capturing such information from the producers' websites if this information was available and was deemed reliable. The data were then assessed using the Balanced Nutrition Index™ (BNI™) technology (see Perezgonzalez, 20111). Missing data for fiber was estimated for the aggregated variable dietBNI from USDA's database (20115).

Data analysis

The sample data was assessed as per normality (see Perezgonzalez, 2012b3). The BNI distribution was significantly non-normal in skewness, even when being quite conservative in such assessment, as per Tabachnick & Fidell (20014) (z=3.39, p<0.001, s=0.001). Extreme values also appeared at both ends of the sample distribution, the most extreme of which was located towards the skewness end, although such values were not out of the ordinary (for example, the 5% trimmed mean, BNI 86.02, was practically similar to the untrimmed mean, BNI 86.50).

The present stage of research on the BNI of foods offers little evidence for ascertaining the real distribution of nutritional balance in the population of food products, including that of potato chips. In theory, the nutritional distribution of well-balanced products would resemble a chi-square distribution, thus, it can be expected that as products move up the scale towards greater unbalance, they may adopt a more normal distribution. Anecdotal evidence of the nutritional distribution of a sample of 1000 food products seems to support such trend towards either a normal distribution or an F-distribution.

Given the uncertainty about the nutritional distribution of potato chips in the population, the sample data was not transformed in any way. Instead, the article provides results to cover both eventualities: on the one hand, that the sample represents the true nature of the population, this being skewed towards higher levels of unbalance, therefore non-parametric results are more appropriate under such assumption; on the other hand, that the population is normally distributed, therefore parametric results are more appropriate under such assumption.

Linearity between variables was adequate.

The main analyses carried out were population inferential statistics using 95% confidence intervals.

SPSS-v18 was used for the computation of variables, including BNI and international indexes, and for inferential statistical analyses.

Generalization potential

The sample was fairly representative of the population of potato chips in New Zealand. Furthermore, most of the products were either produced locally or imported from Australia. The results of this study may, thus, be generalizable to the following populations (in order of decreasing generalization power):

  • New Zealand, nationwide.
  • Australia.
  • Internationally, if one assumes potato chip products to be of approximately similar nutritional composition anywhere.

The results of this study may also be of interest to the following populations:

  • food researchers
  • dietitians
  • food policy makers
  • consumers
1. PEREZGONZALEZ Jose D (2011). Balanced Nutrition Index™ (BNI™). Journal of Knowledge Advancement & Integration (ISSN 1177-4576), 2011, pages 20-21.
2. PEREZGONZALEZ Jose D (2012a). Tasty taytos. The Balanced Nutrition Index (ISSN 1177-8849), 2012, issue 5.
3. PEREZGONZALEZ Jose D (2012b). Nutritional balance of potato chips (descriptive statistics). Journal of Knowledge Advancement & Integration (ISSN 1177-4576), 2012, pages 244-246.
4. TABACHNICK Barbara G & Linda S FIDELL (2001). Using multivariate statistics (4th ed). Allyn & Bacon (Boston, USA), 2001.
5. USDA (2011). Nutrient data for 19411, Snacks, potato chips, plain, salted. USDA National Nutrient Database for Standard Reference, 2011, December 7.
+++ Notes +++
6. The second edition revises the interpretations of unbalance.
7. Thin slices of potatoes fried or baked until crisp, and with added seasoning and flavorings. They may also be known as potato crisps or potato wafers.
8. When interpreting the BNI as 0 = balanced, 1-29 = slightly unbalanced, 30-59 = moderately unbalanced, 60-99 = highly unbalanced, ≥100 = extremely unbalanced.
9. The lower and upper bounds for carbohydrates are reverse in order to keep the total energy count of the resulting profiles as similar as possible. Carbohydrates were selected for this reversal as they are the nutrient typically set by difference, after estimating proteins and fats.

Want to know more?

BNI analysis of individual products
You can access either the BNI™ database or the 'BNI™ journal (2012, issue 5) - Tasty taytos' for individual nutrition analyses of each food product in the sample.
Wiki of Science - More information about nutritional balance
Two Wiki of Science indexes provide easy access to information about foods and BNI-related topics.
Wiki of Science - Nutritional balance of potato chips (further knowledge)
Two Wiki of Science pages provide further introductory and descriptive information about the nutritional balance of potato chips.


Jose D PEREZGONZALEZ (2012). Massey University, Turitea Campus, Private Bag 11-222, Palmerston North 4442, New Zealand. (JDPerezgonzalezJDPerezgonzalez).


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