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I am looking to understand the following table from this article to better understand some statistical stuff.

The article is exploring the outcomes of meat via 3 factors(marinade, temperature and cooking time). And they state the tools used in the statistical analysis as this:

Descriptive and inferential statistics were used according to procedures described by Anderson. [22] The Dixon’s Q-test was applied in order to examine outlier values. A three-factors´ ANOVA was applied to evaluate the influence of the factors (marinade type, cooking temperature, and cooking time). Differences between two means were identified using an unpaired t Student test(P< .05). For multiple comparisons, Fisher´s Least Significant Difference (LSD) test was applied. The significance level was set at P<.05 in all cases. Discriminant analysis was performed to ascertain which of the instrumental parameters (pH, instrumental color and SF) were useful in differentiating among the beef and meat analog samples. Statistical analysis was carried out with Minitab® software (Version 18.1, Minitab Inc., PA, USA).

A couple of things I want to understand from this table are:

  • How are the values in table expressed as Mean (since there is only one measurement) and what are the values in parentheses?
  • What does it mean that different superscripts in the same column differ significantly (P < 0.05)
  • Of the statistical analysis tools that I quoted, which ones produce this table?
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  1. Next to the mean figures in brackets is standard deviation
  2. ANOVA is an omnibus test, that means when you have a significant model F test, this tells you that overall there are differences between groups. You then need to follow this up with a post-hoc procedure (if not doing planned contrasts, i.e., if you have no apriori hypotheses you want to test). The post hoc test the authors in this paper use is Fisher’s LSD multiple comparison test. This compares all the mean values of each group, two at a time. Because the authors are doing multiple comparisons in such a way, the Type 1 error rate is inflated (false positive), so the Fisher’s LSD post-hoc procedure adjusts the signifance level, essentially making it stricter.
  3. Without going into detail and reading the whole paper, it looks like these are the results of the Fisher’s LSD multiple comparison test following up from the significant ANOVA. It looks like the superscript shows a signficant comparisons between groups, e.g. the superscript cd means the authors found a significant difference (at p<0.05) between group c and d when doing a Fisher’s LSD multiple comparison test.
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  • $\begingroup$ Ok, but why is the value before brackets a mean? Isn't it just a single measurement? $\endgroup$ Nov 17 '21 at 19:54
  • $\begingroup$ These are the values of the beef dependent variable (I believe it is called "beef yield" in the article) by whatever group they are in (shown by superscript (cd etc.) See the article text: "Beef samples were only significantly affected by the individual factors cooking time and cooking temperature (P< .05)." The 3 factor ANOVA tests overall if group means differ, the Fisher’s LSD post-hoc procedure is used to compare groups pairwise, and the authors subsequently report only the IVs cooking time and cooking temperature had significant effects. $\endgroup$
    – JoeyyyFunk
    Nov 18 '21 at 11:41
  • $\begingroup$ Yes, but take a look at first row for example, the value $5.60$, why do they call this value a "mean"? What is it a mean of if only a single measurement is performed? Shouldn't there be at least 2 measurements to calculate a mean? $\endgroup$ Nov 18 '21 at 12:33
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    $\begingroup$ It is the mean value calculated from all observations in the experimental group. Looking in the article, it says: "two batches were prepared, which means that the experimental design was replicated twice. For each batch, 1200 g approximately of beef and 1200g approximately of meat analog were used and 24 samples (100 ± 10 g and 1 cm thick) were analyzed". So I am assuming that the mean figure is created based on the results from the two batches. $\endgroup$
    – JoeyyyFunk
    Nov 18 '21 at 14:24

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