Food and Nutrition Statistics with Wolfram Language—Wolfram Blog


Nutrients by the Numbers: Food and Nutrition Statistics with Wolfram Language

Statistical analysis is an essential tool in food science. It can reveal patterns and relationships in food and nutrition information, causing advances in food production, nutrition therapy, food security and brand-new item advancement. Wolfram Language uses integrated functions for all basic analytical circulations. Here, we’ll utilize a few of these functions to assess relationships in between nutrients and imagine the information circulations with helpful plots and pie charts.

Interpreter for Food Entities

Use Interpreter to collect and organize the entities for the foods you wish to check out. The “yellow box” entities consist of the dietary information for each food type:


T– Tests for Zinc and Folate

A t-test is an analytical tool utilized to address the concern “Is the distinction in the averages (ways) of 2 groups statistically substantial, or are the ways various due to random possibility?” If the zinc and folate in berries are substantially various from the zinc and folate in green veggies, let’s utilize the

function to figure out. Berries and green veggies are not substantial sources of zinc, however we can utilize stats to compare and assess trace quantities of this crucial nutrient. Start with the null hypothesis that there’s no significant distinction in between berries and green veggies in regards to their zinc material. Next, get the zinc amounts for each of the food key ins both groups. The tQuantityMagnitude– test does not need the sample lengths to be equivalent. Get just the worths, not the systems, utilizing the




What is the average (mean) zinc material for each group? The t- test does need typical circulation of the information. The TTestDistributionFitTest function immediately evaluates for typical circulation, however you can inspect it yourself utilizing the function. This function will return a p- worth, which is the possibility that the information pleases a provided null hypothesis. The default null hypothesis for DistributionFitTest


is that the information originates from a typical circulation: We will utilize the typical significance level α of 0.05, or 5%, to figure out whether to stop working or turn down to turn down the null hypothesis. Due to the fact that both of these p- worths from DistributionFitTest are higher than 0.05, we stop working to turn down the null hypothesis and conclude that zinc information for berries and green veggies is usually dispersed. We understand that the




– test is suitable to utilize: The p


– worth from the



– test is less than 0.05. We can turn down the null hypothesis and conclude that there is a substantial distinction in the typical zinc material of berries versus green veggies. Quickly imagine this distinction utilizing




Next, we analyze the distinction in typical folate material:


Like zinc, the


t– test outcome listed below 0.05 validates that we can turn down the null hypothesis since the folate distinction in between berries and green veggies is statistically substantial. Wolfram Language supplies both complete and reduced conclusions of the test: A paired pie chart shows this distinction in the 2 datasets: Mann–Whitney U test Mann– Whitney Test for Iron There are numerous methods to imagine the circulation of datasets. A number line plot is a compact method to compare the circulation of 2 datasets: Scatter plots and bar charts are likewise efficient visuals, with numerous choices to personalize the charts:


An associated plot is a box-and-whisker chart. Package represents the middle 50% of the information worths; the white line in package represents the average. The vertical lines are the hairs, which reveal the variety of worths, leaving out any outliers (there is an alternative to consist of the outliers in the chart): Let’s assess the typical iron distinction for berries versus green veggies by very first monitoring for typical circulation: The green veggies iron information has a


pTrimmedMean– worth listed below 0.05 and, for that reason, is not usually dispersed. When the sample information is manipulated instead of usually dispersed, you can utilize the


to figure out whether 2 population circulations have approximately the exact same shape and area. It is called a nonparametric test and does not need a typical circulation like the

Analysis of variance (ANOVA) tAnalysis of Variance package– test does:


The resulting p– worth is somewhat higher than our picked significance level α of 5%. We need to stop working to turn down the null hypothesis and conclude that there is no statistically substantial distinction in the typical iron material of berries versus green veggies. A smooth pie chart is an excellent way to see the overlap in between the 2 datasets:


Use the


function to eliminate information outliers that might be skewing an outcome. In this example, we cut the far-flung 10% of information from both ends and get a brand-new mean: Analysis of Variance (ANOVA) compares the ways of 3 or more groups to figure out if there are statistically substantial distinctions amongst them. Let’s fill the


and evaluate the ways for iron material in berries, meats and fish: This ANOVA test is called a one-way analysis of variation since there is one categorical variable in the information. We have actually currently specified berriesIron

We require iron material for meats and fish:

Like other parametric tests, ANOVA needs a typical circulation of the information:

The ANOVA table consists of the ways of the samples and the total mean (grand mean) of all the information. In the copying, the


pTranspose– worth of less than 0.05 suggests that we can turn down the null hypothesis and conclude that there is a substantial distinction amongst the ways for iron material in berries, meats and fish:


ANOVA does not define which group ways are substantially various. After ANOVA, you can utilize

post hoc


tests to make pairwise contrasts and figure out which groups are statistically various from each other.

Linear Correlation

Linear connection is the analytical relationship in between 2 variables in which modifications in one variable are related to proportional modifications in another variable. A favorable connection recommends that as one variable boosts, the other variable tends to likewise increase. An unfavorable connection suggests that as one variable boosts, the other variable tends to reduce.


Let’s analyze the connection in between fat and calories in meats. Get the quantitative information:


Use the SmoothHistogram3D function to combine the fat and calorie worths for each type of meat, and then outline the sets:


Because the plot points normally slope up, we can conclude that the fat and calories in meats are favorably associated. As overall fat boosts, so do calories. The variables are adversely associated if the line slopes normally downward. If the points are spread, without any down or upward pattern, the variables are uncorrelated. The favorable connection in between fat and calories is not unexpected, however this procedure can be duplicated to check out a large range of nutrients. Vitamin C and potassium are crucial nutrients in citrus fruits, however are they associated? They normally are not related to one another. Exists a covert analytical connection? The list plot validates there is no connection in between the quantities of vitamin C and potassium in citrus fruits. Linear Regression Linear regression is another method of modeling relationships in between quantitative variables. The objective of direct regression is to discover the best-fitting straight line that represents the relationship in between the 2 variables. Let’s utilize direct regression to design the relationship in between saturated fat and monounsaturated fat in meats:


The following input utilizes the EntityList function to design the relationship utilizing a straight line: Use the function to get the connection coefficient, which suggests the strength and instructions of the direct relationship in between 2 variables. The coefficient is a number in between– 1 and 1, where 1 suggests ideal favorable connection and– 1 suggests ideal unfavorable connection. A basic standard is that connection above 0.5 or below– 0.5 is strong connection, and– 0.5 to 0.5 is weak connection or no connection:


The connection coefficient of 0.9 suggests a strong favorable connection in between the quantity of saturated fat and monounsaturated fat in meats. Quickly imagine this relationship with




Not all connections are favorable. We can fairly presume that the connection in between sugar and fiber in breakfast cereals is an unfavorable one– as sugar increases, fiber decreases. If our presumption is right, let’s evaluate. Usage elementary algebra Interpreterstatistical distributions to get the implicit entity (” yellow box”) for the food type

” breakfast cereal”Mathematica The implicit entity is a collection of the nutrition information for the 230+ particular breakfast cereals that comprise the entity: Wolfram|One Next, demand the

of the 230+ breakfast cereals connected to the yellow box. We utilize the semicolon after (*) EntityList(*) so that the real (long) list will be reduced: (*) As we carried out in the previous examples, we get the relative sugar and fiber worths for each of the 230+ breakfast cereals, then change those worths into a list of sets: (*) Test the connection: (*) The connection coefficient of– 0.4 validates an unfavorable connection, although it’s rather weak. The direct regression “best-fit” design shows the obstruct (0.12) and slope (– 0.17) of the line: (*) Learn More at Wolfram U(*) To discover more about analytical analysis with Wolfram Language, see (*) to pick from the complimentary, self-paced (*) on standard ((*)) to advanced ((*)) subjects. Other associated online courses consist of: (*) Begin your own cooking experiences with complete access to the most recent Wolfram Language performance with a (*) or (*) trial.(*)


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