Bar Chart, Line Chart & Spider Plot (with & without Significance)

Bar Chart, Line Chart & Spider Plot (with & without Significance)

Purpose

These modules are used to visualise product differences and are available for sensory and consumer analysis. They are a key part of exploratory data analysis, presenting a visualisation to aid understanding of how products differ.

In EyeOpenR there are three different types of visualisation available: bar charts, line charts and spider plots. Each offers a different presentation of the same information and choice of type of chart is for the user to decide. A table of means is presented with each chart.

There are two choices for each type of chart:

  1.  ‘of means’ presents the chart and a table of the means. These modules also enable these visualisations to be presented separately by other factors such as assessor or session.
  2. ‘with significance’ presents the chart and a table of the means, and assesses the significance of the product differences. This option also reports the results of an ANOVA to assess product differences.

When identical options are selected, the ANOVA results presented with the charts in the ‘with significance’ modules is the same for each of the chart types.

Data Format

  1. Profiling.xlsx
  2. Consumer.xlsx

For EyeOpenR to read your data, the first five columns of the ‘Data’ sheet must be in the following order: assessor (consumer), product, session, replicate and order (sequence). For sensory analysis the data for attributes should be in the sixth column (column F) onwards. There should be one column for each attribute. The attributes data should be numeric. For consumer analysis the data for consumer liking and other consumer assessments (ratings) should be in the sixth column (column F) onwards. There should be one column for each rating. These are described as attributes in the options.

If there is no session, replicate or order information then these columns should contain the value ‘1’ in each cell.

Additional information about the data in the ‘Data’ sheet can be included in additional sheets. The ‘Attributes’ sheet can be used to specify the names of the attributes, data types and minimum and maximum values that are used to check data quality. The ‘Assessors’ sheet can be used to specify assessor names if codes are used in the ‘Data’ sheet. Similarly, the ‘Products’ sheet can be used to specify product names if codes are used in the ‘Data’ sheet. See the example spreadsheet for an illustration of the data format. 

Background

An important step in the understanding of sensory and consumer studies is to visualise the data. This aids understanding of how products relate to attributes or consumer ratings. There are three different types of visualisation available in EyeOpenR: bar charts, line charts and spider plots.

In the data, each product is assessed by many assessors (or consumers) and so the first stage of creating data for the visualisation is to average by taking the mean over the assessors. These means are the values shown in the charts. If the design of the study is unbalanced or if there are missing values, there is the option of plotting adjusted means (adjusted for other effects such as assessor).

Examples of each type of chart are shown and described in detail in the ‘Results and Interpretation’ section. Each one shows the mean score of each attribute or consumer rating for each product. Being able to visualise these means aids the understanding of how products differ.

The modules that are named ‘Chart/Plot with Significance’ go a step further and run an ANOVA model with the aim of testing the size of the product differences relative to the underlying variability. Background information for ANOVA is found in the help for the ANOVA module (where the size of the product differences are also estimated, tested and reported). 

Options (Chart/Plot of Means)

Options for bar charts are in two sections: Analysis options and Split options. The options for the other two types of charts are in a single section and described separately.

Analysis options (Bar Charts)

  1. Treat Sessions/Replicates Separately: There are three options; ‘No’, ‘Sessions’, ‘Replicates’. Only one option can be selected. If either sessions or replicates is selected then the results are presented either for each session or for each replicate. If sessions or replicates are part of the design then one would usually choose ‘No’. If either are selected then either each session or each replicate are treated completely separately and product means are calculated separately.
  2. Type of Mean: There are two options: ‘Adjusted’ presents adjusted means derived from an ANOVA specified using the four options that follow. ‘Arithmetic’ presents unadjusted means and if selected the next four options are greyed out because they are not needed. If the design of the study is balanced and there are no missing values then adjusted and arithmetic means are identical.
  3. Include Assessor Effect: Only available if ‘Adjusted’ means have been selected. Includes assessor effects in the ANOVA and therefore means are adjusted for assessor differences.
  4. Include Session Effect: Only available if ‘Adjusted’ means have been selected. Includes session effects in the ANOVA and therefore means are adjusted for assessor differences.
  5. Include Replicate Effect: Only available if ‘Adjusted’ means have been selected. Includes replicate effects in the ANOVA and therefore means are adjusted for assessor differences.
  6. Include 2-way Interaction: Only available if ‘Adjusted’ means have been selected. If at least one of the preceding three effects has been selected the two-way interaction of product and those effects is also included in the ANOVA. If no other effect has been selected the ANOVA is a 1 way ANOVA with product and this option is ignored.
  7. Number of Decimals for Values: Specify the number of decimal places shown for means.

Split options (Bar Charts)

  1. Split results on: There are five options here; None, Judge, Attribute, Product, Session. If a choice is made other than None the results are presented separately for each level of the split selected. For consumer studies ‘Attribute’ refers to the consumer ratings.
  2. Split results on Values of: EyeOpenR offers options based on data type of other variables that the analysis can be split by. For example, it can be split by levels of one of the attributes.
  3. Split Results on Assessors Metadata: If Assessor metadata is set up then options other than ‘None’ are shown.
  4. Split Results on Products Metadata: : If Products metadata is set up then options other than ‘None’ are shown.

Options (Line charts and Spider plots)

  1. Split results on: There are five options here; None, Judge, Attribute, Product, Session. If a choice is made other than None the results are presented separately for each level of the split selected. For consumer studies ‘Attribute’ refers to the consumer ratings.
  2. Treat Sessions/Replicates Separately: There are three options; ‘No’, ‘Sessions’, ‘Replicates’. Only one option can be selected. If either sessions or replicates is selected then the results are presented either for each session or for each replicate.
  3. Type of Mean: There are two options: ‘Adjusted’ presents adjusted means derived from an ANOVA specified using the four options that follow. ‘Arithmetic’ presents unadjusted means and if selected the next four options are greyed out because they are not needed. If the design of the study is balanced then adjusted and arithmetic means are identical.
  4. Include Assessor Effect: Only available if ‘Adjusted’ means have been selected. Includes assessor effects in the ANOVA and therefore means are adjusted for assessor differences.
  5. Include Session Effect: Only available if ‘Adjusted’ means have been selected. Includes session effects in the ANOVA and therefore means are adjusted for assessor differences.
  6. Include Replicate Effect: Only available if ‘Adjusted’ means have been selected. Includes replicate effects in the ANOVA and therefore means are adjusted for assessor differences.
  7. Include 2-way Interaction: Only available if ‘Adjusted’ means have been selected. If at least one of the preceding three effects has been selected the two-way interaction of product and those effects is also included in the ANOVA. If no other effect has been selected the ANOVA is a 1 way ANOVA with product and this option is ignored.
  8. Number of Decimals for Values: Specify the number of decimal places shown for means.

Options (Chart/Plot with Significance)

The options for charts/plots with significance are identical for all three chart types. The options are split into two sections: General Options and Model. 

General options

  1. Treat Sessions/Replicates Separately: There are three options; ‘No’, ‘Sessions’, ‘Replicates’. Only one option can be selected. If either sessions or replicates is selected then the results are presented either for each session or for each replicate. If sessions or replicates are part of the design then one would usually choose ‘No’ and then they would be part of the ANOVA model specified in the Model Options. If either are selected then either each session or each replicate are treated completely separately and product means are calculated separately.
  2. Type of Mean: There are two options: ‘Adjusted’ presents adjusted means derived from the ANOVA specified using Model Options. ‘Arithmetic’ presents unadjusted means. If the design of the study is balanced then adjusted and arithmetic means are identical. Adjusted means take into account missing data or imbalance in the design based on the ANOVA model.
  3. Number of Decimals for Values: Specify the number of decimal places shown for means.
  4. Number of Decimals for p-values: Specify the number of decimal places shown for p-values in the results.

Model

  1. Assessor Effect: Two options: Yes and No. If Yes is selected then Assessor is included in the ANOVA.
  2. Type of Assessor Effect: If an assessor effect is included, the user must make a choice between two options: Randomize or Fixed. If ‘Randomize’ is selected Assessor is treated as a random effect in the ANOVA and if ‘Fixed’ is selected Assessor is treated as a fixed effect. If  ‘Randomize’ is selected then ensure that ‘Interaction’ is also selected.
  3. Session Effect: If ‘Yes’ is selected then Session effects are included in the ANOVA if there is session information in the data. If the data is not available this is reflected in the Information tab of the results.
  4. Replicate Effect: If ‘Yes’ is selected then Replicate effects are included in the ANOVA if there is replicate information in the data. If the data is not available this is reflected in the Information tab of the results.
  5. Sequence Effect: If ‘Yes’ is selected then Sequence (order) effects are included in the ANOVA if there is sequence information in the data. If the data is not available this is reflected in the Information tab of the results.
  6. Interaction: If ‘Yes’ is selected and at least one of the preceding four effects has been selected the two-way interaction of product and those effects is also included in the ANOVA. If no other effect has been selected the ANOVA is a 1 way ANOVA with product and this option is ignored. If assessor is in the model a mixed-model ANOVA is performed, meaning the calculation of the F-statistic uses the product x assessor interaction as the denominator for product and assessor main effects, not the model residuals. This is preferable because, especially in sensory data, the user wishes to test the product variability against the level of agreement/disagreement within the panel of assessors.
  7. Significance Level: There are six options. The first three options contain three probability levels each. If one of these are chosen the results will signify the significance level of product differences for each attribute (consumer rating for consumer studies) using these three probabilities where p-values less than the smallest probability will be indicated with three stars, the next with two stars and the largest with a single star. For example, if the option 1%:5%:10% is selected and the probability associated with the product effect for attribute A is 0.07 then this attribute would be shown with a single star (*), if p=0.03 the attribute would be shown with two stars (**), and if p=0.001 the attribute would be shown with three stars (***). The remaining three options enable the choice of a single significance level of 1% or 5% or 10%. If one of these are selected the attributes are shown with a single star if the probability associated with the product effect is less than the level selected.

Results and Interpretation

  1. Bar chart (Bar chart of means and Bar chart with significance): This shows the bar chart of means by product and attribute (rating for consumer studies) (see example below), with a table of the data. For the ‘with significance’ module the significance of the product differences for each attribute are indicated on the chart and in the table by the use of stars (*) displayed alongside the attribute name (as described in the ‘Significance level’ option). The bar chart shows a vertical bar for each attribute and product. The bars are grouped and labelled by attribute, with products within each attribute shown in the same order as they are displayed in the legend of the chart (the legend shows the colour of bar used for each product). This order is defined by the order in the data. The order of the attributes on the horizontal axis is also derived from the order of the columns in the data. The length (height) of each bar represents the mean with the longest bars having the highest mean for that product and attribute. Where bars are very different for an attribute this indicates product differences for that attribute. Differences between attributes show the relative strength of the attributes. 
  2. Line chart (Line chart of means and Line chart with significance): This shows the line chart of means by product and attribute (rating for consumer studies) (see example below), with a table of the data. For the ‘with significance’ module the significance of the product differences for each attribute are indicated on the chart and in the table by the use of stars (*) displayed alongside the attribute name (as described in the ‘Significance level’ option). The line chart shows a single line for each product. Each point on the line represents the mean value of that product for the attribute shown on the horizontal axis. The legend shows the colour of line used for each product. The order of the attributes on the horizontal axis is derived from the order of the columns in the data. The height of each point represents the mean with the highest points having the highest mean for that product and attribute. Where the spread of points for an attribute is wide (lines far apart) this indicates product differences for that attribute. Differences in the height of lines between attributes show the relative strength of the attributes. 

  3. Spider plot (Spider plot of means and Spider plot with significance): This shows the spider plot of means by product and attribute (rating for consumer studies) (see example below), with a table of the data. For the ‘with significance’ module the significance of the product differences for each attribute are indicated on the plot and in the table by the use of stars (*) displayed alongside the attribute name (as described in the ‘Significance level’ option). The spider plot is similar to the line chart where the horizontal axis has been turned into a circle with the attributes shown as points on the edge of a circle. The spider plot shows a single line for each product, each line joins points around the circle and therefore has no start and end, and joins with itself to form a 2-dimensional shape. Each point on the line represents the mean value of that product for the attribute shown on the circumference (outer edge) of the circle. Concentric circles inside the circumference of circle are equivalent to the vertical axis on a line chart and represent the mean value of the attributes. The legend shows the colour of line used for each product. The order of the attributes around the outer edge of the circle is derived from the order of the columns in the data. The distance of each point from the centre of the circle represents the mean, with the points closest to the outer edge having the highest mean for that product and attribute. Where the spread of points from the centre to the outer edge for an attribute is wide (lines far apart) this indicates product differences for that attribute. Differences in the distance of points from the centre between attributes show the relative strength of the attributes.   

  4. Information (all modules): This shows any notes or warnings that are relevant to the procedure. For the ‘of means’ modules, if the adjusted means have been selected a description of the ANOVA model is included here.
  5. Only Significant Attributes (‘with significance’ modules): Repeats the bar chart, line chart or spider plot including only those attributes (rating for consumer studies) with significant product effects.
  6. ANOVA p-values (‘with significance’ modules): The ANOVA table showing the p-values associated with the specified ANOVA model. This is colour-coded to aid interpretation.  A sensory researcher may well wish to understand if there are differences between products per attribute (rating for consumer studies): this will be reflected in the ‘Product’ column. In general, the researcher would like significant differences per attribute in the product column, which indicates the sensory panel can discriminate between products on this attribute.  Likewise the ‘Assessor’ and ‘Replica’ column provides information on whether there are differences between assessors and replicates per attribute.  P-values for the requested interaction terms are then presented: small p-values are generally not wanted: e.g., a significant p-value (say p <.05) for the Product:Assessor interaction indicates significant disagreement among the sensory panel concerning that attribute. Product:Replica and Assessor:Replica can be interpreted in similar fashion if they are included in the model. 
  7. ANOVA tables (‘with significance’ modules): Provides Sum of Squares (Sum Sq), Degrees of Freedom (DF), F-value and p-value for each term in the chosen ANOVA model, per attribute (rating for consumer studies).  Sum Sq refers to the total variation in the data. DF inform the user of the number of levels free to vary within each model term. Mean Squares can be calculated by dividing the Sum Sq by the respective DF. The F value, also known as the F ratio, reflects the variability captured by each effect (the Mean Square; i.e., the signal) divided by the Mean Square of the Error (i.e., the noise). The term used for the Mean Square of the Error will differ depending on whether there is a Product-by-Assessor interaction included. If there is a Product-by-Assessor interaction term, the then the Mean Square of the Error will be the Product by Assessor Mean Square. In laymen’s terms, the differences between products on a given attribute are compared to the level of disagreement in the (sensory) panel. If assessors are in disagreement, the Product by Assessor interaction will have a relatively high Sum Sq value and thus a high Product by Assessor Mean Square value. As this is the denominator in the F-value calculation for a Product effect, the high level of disagreement will weaken the Product F value. This will lessen the ability to see significant differences between products. This is one reason why training a panel can improve the power or discriminability of the panel: lowering the level of disagreement amongst the panel lowers the noise, which makes the signal of product differences more salient. The p-value is indicated by the last column and provides the probability of making a Type I error. Thus, if a Product p-value is p < 0.001 on a given attribute, there is a 0.1% chance of concluding a difference between products on this attribute when in reality there is no difference. As this chance is very, very small, the interpretation is that it is very unlikely and thereby the (null) hypothesis that there are no differences between products on the given attribute is rejected. Therefore, the product effect is deemed ‘significant’: there is a difference in intensity (somewhere) between products on this attribute. Typical thresholds to determine significant used in sensory and consumer science are 1, 5 and 10%.   

Technical Information

R packages used:
  1. averagetable (SensoMineR) for calculating the means.
  2. lm (stats) for the model in the ‘with significance’ modules.
  3. Anova (car) for the ANOVA in the ‘with significance' modules.

References

  1. Kemp, S.E., Hollowood, T. & Hort, J. (2009) Sensory Evaluation: A Practical Handbook. Wiley.
  2. Lawless, H. T., & Heymann, H. (2010). Sensory Evaluation of Food: Principles and Practices (2nd ed.). Springer-Verlag.
  3. Lea, P., Næs, T. & Rødbotten, M. (1997). Analysis of Variance for Sensory Data. Wiley. 
  4. O’Mahony, M. (2017). Sensory Evaluation of Food: Statistical Methods and Procedures. Routledge.
  5. Ott, R., & Longnecker, M. (2015). An Introduction to Statistical Methods and Data Analysis (7th edition). Brooks Cole.

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