20130219 - Nutritional balance of corn chips (inferential statistics) (2e) - 2012

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[<Normal page] [PEREZGONZALEZ Jose D (2012). Nutritional balance of corn chips (inferential statistics) (2e)⁶. Knowledge (ISSN 2324-1624), 2013, pages 64-68.] [DOI]

Table of Contents

BNI of corn chips (inferences)

Materials and procedure

Data analysis

Generalization potential

BNI of corn chips (inferences)

Perezgonzalez assessed the nutritional balance of corn chips⁷ in 2012³, as part of a research on the nutritional composition of snacks in New Zealand. This article provides inferential information both about the sample of products under research (foodBNI) as well as about a hypothetical diet based on those products (dietBNI).

foodBNI

The population of corn chips appears as extremely unbalanced⁸ (illustration 1). Indeed, it can be inferred, with a 95% degree of confidence, that the median nutritional balance is located somewhere between BNI 76.67 and BNI 88.63, and the mean sensibly lower, somewhere between BNI 53.17 and BNI 63.07.

Illustration 1: Food's nutritional balance distribution
Non-parametric	BNI	WHO	US/CAN	AUS/NZ	UK
Median CI₉₅ lower	76.67	64.22	77.46	65.68	64.32
Median CI₉₅ upper	88.63	77.00	87.84	75.54	76.90
SPR lower	10.97	12.13	8.88	8.64	12.80
SPR upper	22.93	24.92	19.27	18.50	25.38

Parametric	BNI	WHO	US/CAN	AUS/NZ	UK
Mean CI₉₅ lower	53.17	51.92	41.79	42.58	38.52
Mean CI₉₅ upper	63.07	62.50	50.39	50.73	48.93
SD CI₉₅ lower	11.45	12.24	9.94	9.43	12.05
SD CI₉₅ upper	18.25	19.50	15.84	15.03	19.19
(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 (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
r / rho	BNI	WHO	US/CAN	AUS/NZ	UK
BNI CI₉₅ lower		.984	.950	.950	.934
BNI CI₉₅ upper		1.000	1.000	1.000	1.000
WHO CI₉₅ lower	.984		.954	.950	.934
WHO CI₉₅ upper	1.000		1.000	1.000	1.000
US/CAN CI₉₅ lower	.950	.962		.984	.947
US/CAN CI₉₅ upper	1.000	1.000		1.000	1.000
AUS/NZ CI₉₅ lower	.962	.966	.977		.958
AUS/NZ CI₉₅ upper	1.000	1.000	1.000		1.000
UK CI₉₅ lower	.887	.909	.894	.906
UK CI₉₅ upper	1.000	1.000	1.000	1.000
(95% confidence interval's lower and upper bounds)

dietBNI

As part of a hypothetical diet in which all products contributed the same weight of chips, the resulting nutritional composition would improve somehow although it would still be extremely unbalanced, with 95% confidence of it ranging somewhere between BNI 45.10 and BNI 53.85 (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 sensibly lower under US', Canada's, Australia's and New Zealand's RDIs, and even more so under UK's RDIs, than under WHO's RDIs.

Illustration 3: Diet's nutritional balance
CI₉₅	Protein	Carbs	Sugar	Fat	Sat.fat	Fiber	Sodium
lower	6.5	60.0**	1.9	24.8	7.5	3.7*	0.524
upper	8.0	57.8**	3.1	25.6	9.9	3.7*	0.657
CI₉₅	International RDIs		BNI	WHO	US/CAN	AUS/NZ	UK
lower	(diet, fiber unest.)		54.44	53.84	42.85	42.98	40.71
upper	(diet, fiber unest.)		57.18	55.38	43.33	43.72	36.90

lower	(diet, fiber est.*)		45.10	42.64	33.96	34.50	25.16
upper	(diet, fiber est.*)		53.85	51.38	40.15	40.69	31.34
(Values per 100g; fiber content estimated from Doritos Burn²; *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 (illustrations 4 and 5).

Illustration 4: dietBNI CI₉₅ lower bound

55%
50%		*
45%		*	*
40%		*	*
35%		*	*
30%		*	*
25%		*	*
20%		*	*
15%		*	*
10%		*	*	*
5%	*	*	*	*
mid	p	c	f	fb
max		s	sf		na
5%			*		*
10%			*		*
15%			*		*
20%					*
25%					*

ideal % = grey cells; actual % = asterisk (*)

Illustration 5: dietBNI CI₉₅ upper bound

55%
50%
45%		*	*
40%		*	*
35%		*	*
30%		*	*
25%		*	*
20%		*	*
15%		*	*
10%		*	*	*
5%	*	*	*	*
mid	p	c	f	fb
max		s	sf		na
5%		*	*		*
10%			*		*
15%			*		*
20%			*		*
25%					*
30%					*
35%					*

ideal % = grey cells; actual % = asterisk (*)

Methods

Research approach

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

Design

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

Sample

Stratified sample of 37 corn chip products, including generic and proprietary brands, diverse flavors and other relevant categories (see Perezgonzalez, 2012a²). The actual products were collected in a convenient manner from four major national supermarket chains. Notwithstanding this, the final sample covered a large proportion of the population of corn chip products available at such supermarkets. Thus, given the scope of the sample and the national coverage of the retail chains behind the sampled supermarkets, the actual sample is fairly representative of the population of corn chips available to New Zealanders nationwide. It may also partially inform about the population of corn 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

Variables of interest for this research were the following:

Weight contribution of seven nutrients (protein, carbohydrate, sugar, fat, 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 hypothetical diets (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 were estimated for the aggregated variable dietBNI from 'Doritos Burn', the product with the lowest fiber content.

Data analysis

The data were assessed as per normality (see Perezgonzalez, 2012b³) and linearity. The BNI distribution was somehow non-normal in skewness, although not significantly so when being rather conservative in such assessment, as per Tabachnick & Fidell (2001⁵) (z=-0.98, p=0.33, s=0.001). Furthermore, there were no extreme values in the variables of interest.

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 corn 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 about the nutritional distribution of a sample of 1000 food products seems to support such trend towards either a normal distribution or an F-distribution. Notwithstanding this, the nutritional distribution of corn chips resembles an F-distribution but in the opposite direction than than expected from theory, with a rather long tail towards less unbalanced products.

Given the uncertainty about the nutritional distribution of corn 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 lower levels of unbalance, even when no significantly so; therefore non-parametric results are more appropriate under such assumption. On the other hand, the population is normally distributed, therefore parametric results are more appropriate under such assumption.

In regards to linearity between relevant variables, the linear model was statistically significant, thus suggesting its use was adequate for capturing the true relationship between variables.

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 corn 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 corn 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

References

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). Corn utopia. The Balanced Nutrition Index (ISSN 1177-8849), 2012, issue 6.

3. PEREZGONZALEZ Jose D (2012b). Nutritional balance of corn chips (descriptive statistics) (3e). Knowledge (ISSN 2324-1624), 2013, pages 56-59.

4. PEREZGONZALEZ Jose D (2012c). Nutritional balance of corn chips (inferential statistics). Journal of Knowledge Advancement & Integration (ISSN 1177-4576), 2012, pages 282-286.

5. TABACHNICK Barbara G & Linda S FIDELL (2001). Using multivariate statistics (4^th ed). Allyn & Bacon (Boston, USA), 2001.

+++ Notes +++

6. This second edition updates the previous one⁴ by revising the interpretations of unbalance.

7. They include both corn chips and tortilla chips. Thus, they can be defined as thin shapes of pressed cornmeal (usually cut into triangles or circles), and then oven-baked or deep-fried.

8. When interpreting the BNI as 0 = balanced, 1-9 = slightly unbalanced, 10-19 = moderately unbalanced, 20-29 = highly unbalanced, ≥30 = 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 corn chip products: You can access either the BNI™ database or the 'BNI™ journal (2012, issue 6) - Corn utopia' 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 corn chips (further knowledge): Two Wiki of Science pages provide further introductory and descriptive information about the nutritional balance of corn chips.

Outdated versions

PEREZGONZALEZ Jose D (2012). Nutritional balance of corn chips (inferential statistics). Journal of Knowledge Advancement & Integration (ISSN 1177-4576), 2012, pages 282-286.