# Assessing the Reliability of Optimized Residual Feed Intake Measurements in Beef Cattle

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

## 1. Introduction

_{s}) is a logical index for comparing alternative RFIs (y

_{i}) to the gold-standard RFI (x

_{i}). On the other hand, the interpretation of r

_{s}is not easy, with the crucial question being what is the lowest acceptable value below 1 for r

_{s}? Scatterplots of ranks (y

_{i}on x

_{i}) may help to illustrate the situation, but do not quantify the transitions in rank in a straightforward way. An alternative to Spearman’s rank-order correlation coefficient is Kendall’s rank-order correlation coefficient τ (or more precisely, its estimate t), which is based on the number of concordant (or ‘agreement’) and discordant (or ‘disagreement’) pairs, i.e., ‘the difference between the probability that, in the observed data, X and Y are in the same order and the probability that the X and Y data are in different order’ [13]. For example, t = 0.90 means that 95% of the pair-wise orders of the animals remain the same (and 5% do not). This is also our a priori threshold for an acceptable t.

_{s}between the alternative RFIs and gold-standard RFIs mean in practice, as we reduce the data used for calculating RFI step-by-step. In many RFI studies, experimental animals have been classified into low-, medium-, and high-RFI groups according to their RFI values, with equal numbers of animals in each of these groups. This ‘thirds approach’ is particularly common in studies on associations between RFI, physiology, and behavior of the animals [14,15,16]. Thus, our aim was also to demonstrate how the reduction of data affects this classification. We introduce ‘the consistency of the thirds’ to assess the consequences of this reduction. Here, we were particularly interested in the probability of the animals remaining in the lowest third (with the best feed efficiency), and our a priori threshold for an acceptable situation was 90%.

## 2. Materials and Methods

#### 2.1. Animals, Management, Feeding and Measurements

^{2}per bull. The rear half of the pen area was a peat-bedded lying area, and the fore half was a feeding area with a solid concrete floor. The bulls had free access to water throughout the experiments. The animals were managed according to Finnish legislation regarding the use of animals in scientific experimentation.

^{2}) were measured at the 1st lumbar vertebrae as described by Huuskonen and Pesonen [21] with a Pie 200 SLC scanner (FPS 8; DFR 2–4 inches) equipped with the QUIP (Quality Ultrasound Indexing Program) software (Version 2.6) and an ASP-18 transducer (3.5 MHz) without a stand-off pad. The average age and live weight at the beginning of the experiment, ADG, average DMI, and MMBW of the experiments, live weight at the end of the experiment, and ultrasound measurements at the beginning (experiments 2 and 3) and end (all experiments) of the experiments are given in Table 4.

#### 2.2. Modelling and Comparing RFI Values

_{i}is the error term, which is for the fitting assumed to be independent and normally distributed. For experiment 1, all 110 animals were included in the fit. For experiment 2, two of the 110 animals were removed as significant outliers. For experiment 3, 4 of the 104 animals were removed. Removing the outliers improved the R

^{2}values of the fits from 0.26 to 0.42 for experiment 2 and from 0.46 to 0.63 for experiment 3. In experiment 2, the two outliers were NR bulls with one having an exceptionally high average DMI of 13.3 kg/d over the experiment, while the other outlier had one of the lowest DMI values at 5.4 kg/d while simultaneously being in the highest quartile of MMBW. The ADG values for the two outliers did not significantly deviate from the average. For experiment 3, the four outliers were AA bulls with one outlier having the lowest average DMI by far at 5.3 kg/d (the second lowest had 6.5 kg/d) while the three other outliers had DMI intake values in the lower quartile, varying between 6.6 and 7.0 kg/d, while having MMBW values in the upper quartile between 91 kg and 97 kg. As in experiment 2, the outliers had rather average ADG values. As a safety measure, the analysis was also run with complete data and the conclusions did not change.

^{2}value calculated using the formula

_{i}with respect to the gold-standard S1, i.e., using the full dataset. Comparisons were carried out in three ways: By calculating two rank-order correlations, Spearman’s correlations, and Kendall’s correlations between the S1 residuals and S2–S15 residuals, and by comparing the transition probabilities between the upper, middle, and lower thirds. The transition probabilities between the thirds were calculated by taking 10

^{5}re-samplings (also known as bootstrap samples [22]) of the animals with a replacement and making fits for S1–S15 for each sample. A small random term was used, so that the resampling would not result in equal ranks, which would make the determination of the thirds problematic. The transition probabilities ${P}_{XY}$ were then calculated as the average fraction of animals that were in the third X in S1 and third Y in the comparative standard.

## 3. Results

#### 3.1. Additional Covariates

^{2}values are presented in Figure 1 for the three experiments. The estimates, standard errors, and p-values for the model with BF and LM at the end of the experiment are given in Table 5. For experiments 1 and 3, the best-fitting model based on adjusted R

^{2}and AIC values is the simplest model without the BF and LM. The adjusted R

^{2}values for these two datasets varied between 0.61 and 0.63. For experiment 2, the models with the LM (either at the end or the average of the beginning and end values) fitted slightly better, with adjusted R

^{2}values of 0.44, compared to 0.42 of the model with only the MMBW and ADG as covariates. However, the p-value of the LM term was 0.02–0.04 in the two alternative models without the BF term, which is not strong evidence given that the models were fitted to three distinct datasets. A simple Bonferroni correction, without even considering the multiple parameters in the model, [24] to the p-values would result in an adjusted p-value of 0.06–0.12, i.e., the result is not statistically significant after adjusting for the three separate fits.

#### 3.2. Reducing the Number of Times Weighed or the Duration of the Test Period

^{2}values are given for experiment 2 in Table 6 and experiment 3 in Table 7. For experiment 2, the estimates and R

^{2}values are not meaningfully different (R

^{2}: 0.41–0.42) for S1, S2, and S3, which have the same observation period but differ in the number of times the animals were weighed. Standards S4–S15 show some notable deviations in the estimates, with S6/12, S7, and S11 standing out with their low R

^{2}values (R

^{2}: 0.30–0.34) as compared to S1. Experiment 3 tells a similar story, with the results for S1, S2, and S3 being consistent (R

^{2}= 0.62–0.63) but S4–S15 deviating more either with respect to the estimates or the R

^{2}value. In particular, S7, S8, S11, and S15 stand out with their relatively low R

^{2}values (0.40–0.50).

_{s}and Kendall’s correlation estimate t, with values pf r

_{s}= 0.98–0.99 and t = 0.89–0.91 for S1 vs. S2, and r

_{s}= 0.97–0.98 and t = 0.86–0.88 for S1 vs. S3. For other standards, Spearman’s correlation is below 0.9 and Kendall’s correlation is below 0.8, which can be chosen as (somewhat arbitrary) numerical limits, in at least one of the experiments. While choosing a numerical limit for Spearman’s correlation is difficult because the values are not intuitive, the choice of 0.8 as a limit for Kendall’s correlation is easier to argue. For example, Kendall’s t of 0.8 would correspond to a situation where our ranking of two cows works 90% of the time and 10% of the time it fails. For experiment 2, the worst performers as measured by t were S7, S9, and S11 with t < 0.65, and for experiment 3, were S4 and S7 with t < 0.5. For experiment 2, which was the slightly shorter experiment, even the worst standards had correlations of r

_{s}= 0.78 or t = 0.60 with the golden-standard RFIs, while for experiment 3, the values were as low as r

_{s}= 0.60 or t = 0.43.

## 4. Discussion

#### 4.1. Additional Covariates

#### 4.2. Reducing the Number of Times Weighed or the Duration of the Test Period

_{s}has been used widely. Either r

_{s}= 0.90 [9] or 0.95 [4,7,10,11] has been regarded as the threshold for acceptable reliability. Gilpin [33] presents a tau-to-rho conversion formula (and tables) for meta-analytic purposes, i.e., for obtaining approximate r

_{s}values if one knows the t values only. The accuracy of the approximation is best for large samples from bivariate normal populations. According to the conversion table presented by Gilpin [33], the acceptance limits of 0.90 and 0.95 for r

_{s}correspond to t-values 0.73 and 0.81, respectively. Thus, our threshold for sufficient reliability (t = 0.90) was more stringent than in the earlier studies.

_{s}, and, for example, r

_{s}= 0.90 corresponds to C% = 87% and r

_{s}= 0.95 to C% = 91%.

_{s}as the only criteria for assessing acceptable reliability. In addition, the thresholds can be also situation specific and benefit from an inspection of the data in more detail in a way that better considers the specific aims of measuring RFI in a certain situation. This is illustrated nicely by Castilhos et al. [11] who showed that shortening the test period from 122 d to 84 d (r

_{s}= 0.954) led to only one out of eleven animals losing their ‘Elite classification’ status, whereas shortening the period to 54 d (r

_{s}= 0.879) resulted in four animals losing this status. In fact, the approach presented by Castilhos et al. [11] resembles our ‘consistency of the thirds’ approach, since our approach could be extended to use any quantiles suited best to a specific situation. Finally, the ‘consistency of the thirds’ approach also gives a simple probability that is easy to interpret while assessing the reliability of the alternative methods as compared to the gold standard.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The adjusted R

^{2}values and the Akaike Information Criterion (AIC) for the fitted models with mid-test metabolic body weight (MMBW, kg) and average daily gain (ADG, kg/d), and models where various combinations of the sub-cutaneous back fat thickness (BF, mm) and the cross-sectional area of longissimus dorsi muscle (LM, cm

^{2}) are included. END refers to measurement at the end of the experimental period and AVG to an average of measurements at the end and beginning of the experimental period.

**Table 1.**Chemical compositions and feeding values of the total mixed rations used in experiments 1, 2, and 3.

Variable | Experiment 1 | Experiment 2 | Experiment 3 |
---|---|---|---|

Dry matter (DM), g/kg | 413 | 438 | 578 |

Crude protein, g/kg DM | 123 | 118 | 120 |

Neutral detergent fiber, g/kg DM | 404 | 351 | 423 |

Metabolizable energy, MJ/kg DM | 11.8 | 11.5 | 11.1 |

Metabolizable protein, g/kg DM | 86 | 85 | 82 |

**Table 2.**Timeline and comparisons of the standards (or data subsets) (S1–15) of experiment 2 with dairy breed bulls (55 Holstein and 55 Nordic Red dairy bulls). Standards S1–15 varied in terms of the duration of test periods (d) and the number of times the animals were weighed (W). Note that in the description of the standards, D refers to the total duration of the test period for standards S1–15 and d refers to the order of the days in S1. Start day of the experiment (d 1) was the day when feed intake measurements were initiated. The grey shading indicates the periods from which the daily dry matter intake data were used. The numbers in the cells of each data subset indicate the weighing days for that test period.

Timeline of Experiment 2 | |||||||||
---|---|---|---|---|---|---|---|---|---|

Period or Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | End |

Period start date | 26 Sep | 2 Oct | 9 Oct | 16 Oct | 23 Oct | 30 Oct | 6 Nov | 13 Nov | 20 Nov |

Period end date | 1 Oct | 8 Oct | 15 Oct | 22 Oct | 29 Oct | 5 Nov | 12 Nov | 19 Nov | - |

Period length, days (d) | 6 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | - |

Weighing days | 1 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 |

Comparisons | |||||||||

S1 = Gold standard ^{1} | |||||||||

S1: D 55 (d 1–55) W9 | 1 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 |

S2: D 55 (d 1–55) W5 | 1 | 14 | 28 | 42 | 56 | ||||

S3: D 55 (d 1–55) W3 | 1 | 28 | 56 | ||||||

S4: D 49 (d 7–55) W8 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | |

S5: D 42 (d 14–55) W7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | ||

S6: D 35 (d 21–55) W6 ^{2} | 21 | 28 | 35 | 42 | 49 | 56 | |||

S7: D 28 (d 28–55) W5 | 28 | 35 | 42 | 49 | 56 | ||||

S8: D 48 (d 1–48) W8 | 1 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | |

S9: D 41 (d 1–41) W7 | 1 | 7 | 14 | 21 | 28 | 35 | 42 | ||

S10: D 34 (d 1–34) W6 ^{3} | 1 | 7 | 14 | 21 | 28 | 35 | |||

S11: D 27 (d 1–27) W5 | 1 | 7 | 14 | 21 | 28 | ||||

S12: D 35 (d 21–55) W6 ^{2} | 21 | 28 | 35 | 42 | 49 | 56 | |||

S13: D 34 (d 1–34) W6 ^{3} | 1 | 7 | 14 | 21 | 28 | 35 | |||

S14: D 35 (d 14–48) W6 | 14 | 21 | 28 | 35 | 42 | 49 | |||

S15: D 35 (d 7–41) W6 | 7 | 14 | 21 | 28 | 35 | 42 |

^{1}Comprises all available measurements.

^{2}S6 = S12.

^{3}S10 = S13. The grey shading for indicating the periods from which the daily dry matter intake data were used.

**Table 3.**Timeline and comparisons of the standards (or data subsets) (S1–15) of experiment 3 with beef breed bulls (52 Aberdeen Angus and 52 Simmental). Standards S1–15 varied in terms of the duration of test periods (d) and the number of times the animals were weighed (W). Note that in the description of the standards, D refers to the total duration of the test period for standards S1–15 and d refers to the order of the days in S1. Start day of the experiment (d 1) was the day when feed intake measurements were initiated. The grey shading indicates the periods from which the daily dry matter intake data were used. The numbers in the cells of each data subset indicate the weighing days for that test period.

Timeline of Experiment 3 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Period, Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | End |

Period start date | 13 Nov | 20 Nov | 26 Nov | 3 Dec | 10 Dec | 17 Dec | 23 Dec | 31 Dec | 7 Jan | 14 Jan |

Period end date | 19 Nov | 25 Nov | 2 Dec | 9 Dec | 16 Dec | 22 Dec | 30 Dec | 6 Jan | 13 Jan | - |

Period length, day (d) | 7 | 6 | 7 | 7 | 7 | 6 | 8 | 7 | 7 | - |

Weighing days | 1 | 8 | 14 | 21 | 28 | 35 | 41 | 49 | 56 | 63 |

Comparisons | ||||||||||

S1 = Gold standard ^{1} | ||||||||||

S1: D 62 (d 1–62) W10 | 1 | 8 | 14 | 21 | 28 | 35 | 41 | 49 | 56 | 63 |

S2: D 62 (d 1–62) W5 | 1 | 14 | 28 | 41 | 63 | |||||

S3: D 62 (d 1–62) W3 | 1 | 28 | 63 | |||||||

S4: D55 (d 8–62) W9 | 8 | 14 | 21 | 28 | 35 | 41 | 49 | 56 | 63 | |

S5: D 49 (d 14–62) W8 | 14 | 21 | 28 | 35 | 41 | 49 | 56 | 63 | ||

S6: D 42 (d 21–62) W7 ^{2} | 21 | 28 | 35 | 41 | 49 | 56 | 63 | |||

S7: D 35 (d 28–62) W6 | 28 | 35 | 41 | 49 | 56 | 63 | ||||

S8: D 55(d 1–55) W9 | 1 | 8 | 14 | 21 | 28 | 35 | 41 | 49 | 56 | |

S9: D 48(d 1–48) W8 | 1 | 8 | 14 | 21 | 28 | 35 | 41 | 49 | ||

S10: D 40 (d 1–40) W7 ^{3} | 1 | 8 | 14 | 21 | 28 | 35 | 41 | |||

S11: D 34 (d 1–34) W6 | 1 | 8 | 14 | 21 | 28 | 35 | ||||

S12: D 42 (d 21–62) W7 ^{2} | 21 | 28 | 35 | 41 | 49 | 56 | 63 | |||

S13: D 40 (d 1–40) W7 ^{3} | 1 | 8 | 14 | 21 | 28 | 35 | 41 | |||

S14: D 42 (d 14–55) W7 | 14 | 21 | 28 | 35 | 41 | 49 | 56 | |||

S15: D 41 (d 8–48) W7 | 8 | 14 | 21 | 28 | 35 | 41 | 49 |

^{1}Comprises all available measurements.

^{2}S6 = S12.

^{3}S10 = S13. The grey shading for indicating the periods from which the daily dry matter intake data were used.

**Table 4.**Age, live weight, ultrasound traits, growth, dry matter intake, and metabolic body weight of the bulls in three experiments.

Experiment 1 | Experiment 2 | Experiment 3 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | SD ^{1} | Min | Max | Mean | SD | Min | Max | Mean | SD | Min | Max | |

At the beginning of the experiment | ||||||||||||

Age, d | 230 | 17 | 164 | 265 | 188 | 7 | 176 | 218 | 204 | 18 | 164 | 261 |

Live weight, kg | 325 | 55 | 198 | 486 | 265 | 24 | 215 | 341 | 347 | 56 | 235 | 548 |

Ultrasound backfat, mm | 1.56 | 0.47 | 0.63 | 3.95 | 2.57 | 0.53 | 1.31 | 3.92 | ||||

Ultrasound ribeye area, cm^{2} | 44 | 5 | 30 | 57 | 56 | 9 | 35 | 83 | ||||

At the end of the experiment | ||||||||||||

Live weight, kg | 396 | 59 | 264 | 584 | 328 | 27 | 267 | 398 | 432 | 61 | 310 | 644 |

Ultrasound backfat, mm | 3.20 | 1.06 | 1.61 | 6.28 | 1.49 | 0.37 | 0.67 | 2.96 | 3.39 | 0.77 | 1.96 | 5.57 |

Ultrasound ribeye area, cm^{2} | 60 | 10 | 39 | 82 | 48 | 5 | 33 | 61 | 68 | 9 | 44 | 87 |

Average during the test period | ||||||||||||

Daily gain, kg/d | 1.23 | 0.21 | 0.73 | 1.72 | 1.13 | 0.18 | 0.61 | 1.61 | 1.34 | 0.21 | 0.94 | 2.06 |

Dry matter intake, kg/d | 8.50 | 1.18 | 3.91 | 11.84 | 7.83 | 0.97 | 4.56 | 10.32 | 8.63 | 1.19 | 6.49 | 12.03 |

Metabolic body weight, kg | 82 | 10 | 59 | 111 | 71 | 5 | 55 | 84 | 87 | 10 | 67 | 119 |

^{1}Standard deviation.

**Table 5.**Estimates, standard errors (SE), and p-values for the regression coefficients with a full model including all measured variables. The sub-cutaneous back fat thickness (BF, mm) and cross-sectional area of longissimus dorsi muscle (LM, cm

^{2}) measurements are those measured at the end of the experiment since those values were available for all three experiments. For experiments 2 and 3, the model was also fitted using the average BF and LM values. The results were largely the same, except that the p-value of BF in experiment 2 was 0.04.

Experiment | Coefficient | Estimate | SE | p-Value |
---|---|---|---|---|

1 | (Intercept) | 0.13 | 0.66 | 0.84 |

ADG ^{1} | 1.37 | 0.38 | <0.001 *** | |

MMBW ^{2} | 0.084 | 0.013 | <0.001 *** | |

LM | −0.003 | 0.013 | 0.84 | |

BF | −0.034 | 0.071 | 0.64 | |

2 | (Intercept) | 0.23 | 0.97 | 0.81 |

ADG | 2.39 | 0.38 | <0.001 *** | |

MMBW | 0.078 | 0.016 | <0.001 *** | |

LM | −0.037 | 0.016 | 0.02 * | |

BF | 0.17 | 0.18 | 0.33 | |

3 | (Intercept) | −0.53 | 0.73 | 0.47 |

ADG | 1.88 | 0.39 | <0.001 *** | |

MMBW | 0.071 | 0.013 | <0.001 *** | |

LM | 0.008 | 0.014 | 0.55 | |

BF | −0.028 | 0.100 | 0.78 |

^{1}Average daily gain (kg/d).

^{2}Mid-test metabolic body weight (kg). *: p<0.05; ***: p<0.001.

**Table 6.**Regression coefficients, their standard errors (SE), and the R

^{2}value for different measurement standards (S1–15, see Table 2 for the details of the standards) based on the data from experiment 2.

S | (Intercept) | ADG ^{1} | MMBW ^{2} | SE (Intercept) | SE (ADG) | SE (MMBW) | ${{R}}^{2}$-Value |
---|---|---|---|---|---|---|---|

1 | 0.010 | 2.592 | 0.069 | 1.113 | 0.442 | 0.017 | 0.42 |

2 | −0.205 | 2.707 | 0.070 | 1.127 | 0.459 | 0.017 | 0.42 |

3 | 0.027 | 2.671 | 0.067 | 1.137 | 0.451 | 0.017 | 0.41 |

4 | −0.332 | 2.362 | 0.079 | 1.161 | 0.446 | 0.017 | 0.39 |

5 | −0.673 | 2.238 | 0.088 | 1.228 | 0.432 | 0.017 | 0.37 |

6/12 | −0.230 | 2.012 | 0.087 | 1.302 | 0.414 | 0.018 | 0.32 |

7 | −0.109 | 1.753 | 0.092 | 1.345 | 0.348 | 0.018 | 0.30 |

8 | 0.252 | 2.297 | 0.072 | 1.045 | 0.373 | 0.016 | 0.45 |

9 | 0.692 | 2.422 | 0.064 | 1.160 | 0.408 | 0.018 | 0.41 |

10/13 | 0.922 | 1.850 | 0.069 | 1.016 | 0.299 | 0.016 | 0.46 |

11 | 0.593 | 1.499 | 0.078 | 1.221 | 0.318 | 0.019 | 0.34 |

14 | −0.601 | 2.136 | 0.091 | 1.209 | 0.379 | 0.017 | 0.39 |

15 | 0.041 | 2.105 | 0.080 | 1.147 | 0.379 | 0.017 | 0.41 |

^{1}Average daily gain (kg/d).

^{2}Mid-test metabolic body weight (kg).

**Table 7.**Regression coefficients, their standard errors (SE), and the R

^{2}value for different measurement standards (S1–15, see Table 3 for the details of the standards) based on the data from experiment 3.

S | (Intercept) | ADG ^{1} | MMBW ^{2} | SE (Intercept) | SE (ADG) | SE (MMBW) | ${{R}}^{2}$-Value |
---|---|---|---|---|---|---|---|

1 | −0.515 | 1.841 | 0.077 | 0.714 | 0.380 | 0.008 | 0.63 |

2 | −0.204 | 1.678 | 0.076 | 0.712 | 0.384 | 0.009 | 0.62 |

3 | −0.131 | 1.699 | 0.074 | 0.708 | 0.373 | 0.009 | 0.62 |

4 | −1.591 | 2.574 | 0.079 | 0.963 | 0.493 | 0.011 | 0.55 |

5 | −0.365 | 2.045 | 0.074 | 0.705 | 0.373 | 0.009 | 0.64 |

6/12 | −0.163 | 2.354 | 0.067 | 0.788 | 0.389 | 0.010 | 0.60 |

7 | 0.408 | 1.688 | 0.074 | 1.072 | 0.474 | 0.013 | 0.40 |

8 | −0.491 | 1.555 | 0.081 | 0.928 | 0.455 | 0.010 | 0.50 |

9 | −0.435 | 1.467 | 0.083 | 0.714 | 0.330 | 0.008 | 0.62 |

10/13 | −0.068 | 1.227 | 0.082 | 0.808 | 0.338 | 0.009 | 0.53 |

11 | −0.277 | 0.796 | 0.090 | 0.942 | 0.366 | 0.011 | 0.46 |

14 | −0.362 | 1.591 | 0.082 | 0.812 | 0.396 | 0.009 | 0.56 |

15 | −0.797 | 1.495 | 0.088 | 0.948 | 0.398 | 0.011 | 0.50 |

^{1}Average daily gain (kg/d).

^{2}Mid-test metabolic body weight (kg).

Standard | $\mathbf{Spearman}\text{\u2019}\mathbf{s}\text{}{\mathit{r}}_{\mathit{s}}$ (Experiment 2) | $\mathbf{Spearman}\text{\u2019}\mathbf{s}\text{}{\mathit{r}}_{\mathit{s}}$ (Experiment 3) | Kendall’s $\mathit{t}$ (Experiment 2) | Kendall’s $\mathit{t}$ (Experiment 3) |
---|---|---|---|---|

2 | 0.98 | 0.99 | 0.89 | 0.91 |

3 | 0.97 | 0.98 | 0.86 | 0.88 |

4 | 0.90 | 0.63 | 0.75 | 0.49 |

5 | 0.87 | 0.95 | 0.68 | 0.82 |

6/12 | 0.84 | 0.74 | 0.65 | 0.56 |

7 | 0.79 | 0.60 | 0.60 | 0.43 |

8 | 0.91 | 0.67 | 0.76 | 0.51 |

9 | 0.78 | 0.98 | 0.62 | 0.88 |

10/13 | 0.84 | 0.86 | 0.66 | 0.67 |

11 | 0.82 | 0.82 | 0.63 | 0.64 |

14 | 0.88 | 0.82 | 0.70 | 0.63 |

15 | 0.86 | 0.65 | 0.68 | 0.50 |

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## Share and Cite

**MDPI and ACS Style**

Mononen, J.; Kostensalo, J.; Pesonen, M.; Huuskonen, A.; Manni, K.
Assessing the Reliability of Optimized Residual Feed Intake Measurements in Beef Cattle. *Ruminants* **2022**, *2*, 407-419.
https://doi.org/10.3390/ruminants2040028

**AMA Style**

Mononen J, Kostensalo J, Pesonen M, Huuskonen A, Manni K.
Assessing the Reliability of Optimized Residual Feed Intake Measurements in Beef Cattle. *Ruminants*. 2022; 2(4):407-419.
https://doi.org/10.3390/ruminants2040028

**Chicago/Turabian Style**

Mononen, Jaakko, Joel Kostensalo, Maiju Pesonen, Arto Huuskonen, and Katariina Manni.
2022. "Assessing the Reliability of Optimized Residual Feed Intake Measurements in Beef Cattle" *Ruminants* 2, no. 4: 407-419.
https://doi.org/10.3390/ruminants2040028