Chapter 3: Analyse scientific research findings

Scientific research in animal production generates valuable data that require careful analysis to extract meaningful findings. Analyzing research findings enables animal production professionals to make informed decisions, optimize livestock management practices, and improve productivity sustainably. In the Kenyan context, where livestock farming is a critical economic activity for many smallholder farmers and commercial enterprises, interpreting data accurately can influence policy formulation, enhance breeding programs, and support disease control strategies. This chapter focuses on identifying and understanding data analysis findings within animal production research.

3.1 Identifying data analysis methods

Before any figure is calculated, the researcher decides which method suits the question and the data. In livestock research the question may be whether three feed rations give different weight gains, what a typical daily milk yield is, or how much birth weights vary within a herd. The method follows from the question and from the kind of data collected: a method that does not fit gives numbers that look exact but answer nothing. This topic names the methods a research technician must be able to recognise and choose: ANOVA, measures of central tendency and measures of dispersion. Carrying out the calculations on a full data set is the work of Perform data analysis.

Data types and the analysis they call for

Quantitative data are numbers from measurement or counting, such as milk yield in litres, weight gain in kilograms per day, feed intake or the number of kids born per litter. Continuous values (body weight) and discrete values (number of kids) are both analysed with statistical tests. Qualitative data describe qualities or categories, such as breed, the severity of a disease sign or a farmer's reason for keeping goats. Nominal categories (breed) have no order; ordinal categories (mild, moderate, severe) do. Qualitative data are usually summarised with counts, percentages and themes, not with means.

Quantitative data also differ in distribution. Values that cluster symmetrically around the middle are approximately normal, while a few very high or very low values make a distribution skewed. The shape decides whether the mean or the median is the better summary and whether a method such as ANOVA can be trusted.

Matching the question to the method

• Do the group means differ? Use ANOVA when there are three or more groups, such as three rations or three breeds.
• What is a typical value? Use the mean, median or mode.
• How much do values vary? Use the range, variance, standard deviation, coefficient of variation or interquartile range.
• Do two measurements move together? Correlation measures how strongly feed intake and growth rate are related, and regression describes how one changes with the other.
• How does a value change over time? Time series methods show seasonal patterns, such as calving or milk yield rising and falling through the year.

Recognising the method first also protects the study from avoidable errors. A mean calculated for breed names, or an ANOVA run on two or three animals per group, is the kind of mistake that careful method selection prevents.

3.1.1 ANOVA

Analysis of variance (ANOVA) is a statistical method that compares the means of three or more groups to find out whether at least one differs from the others by more than chance would explain. Comparing groups two at a time with repeated tests raises the risk of a false finding, so ANOVA tests all groups together in one step. In animal production it is used to judge the effect of rations, breeds or management practices on outcomes such as milk yield, weight gain or litter size.

Purpose of ANOVA

ANOVA separates the variation between groups (caused by the treatment, such as the ration) from the variation within groups (caused by differences between individual animals and by chance). When the variation between groups is large compared with the variation within groups, the treatment probably has a real effect. Example: a researcher feeds three rations to calves on a dairy farm and uses ANOVA to decide whether daily weight gain differs among the rations.

Types of ANOVA

• One-way ANOVA: compares the means of one factor with several levels, such as the average milk yield of three breeds.
• Two-way ANOVA: studies two factors together, such as breed and feeding regime, and shows whether they act separately or interact.
• Repeated measures ANOVA: is used when the same animals are measured several times, such as the milk yield of the same cows each month of a lactation.

Assumptions underlying ANOVA

• Normality: values within each group are approximately normally distributed.
• Equal variances: the spread within the groups is similar.
• Independence: each observation is independent of the others, so animals sharing a pen are not treated as unrelated when the pen itself affects the result.
• Random sampling: animals are chosen and allocated to groups at random so that the groups represent the population.

When these assumptions are broken, for example by allocating the heaviest calves to one ration, the result is biased and cannot be trusted.

Steps in applying ANOVA

1. State the null hypothesis: the group means are equal.
2. Record the data of each group in a table.
3. Calculate the mean of each group and the grand mean of all observations.
4. Calculate the sum of squares between groups: for each group, multiply the number of animals by the squared difference between the group mean and the grand mean, then add the results.
5. Calculate the sum of squares within groups: add the squared differences between each observation and its own group mean.
6. Divide each sum of squares by its degrees of freedom to get the mean squares: groups minus 1 for between groups, total observations minus groups for within groups.
7. Calculate F = mean square between ÷ mean square within.
8. Compare F with the critical value from an F table at the 5% level, or read the p-value from the output. If F is larger than the critical value, or the p-value is below 0.05, reject the null hypothesis.

Worked example

Twelve calves are shared equally among three rations A, B and C. Their daily weight gains in kilograms are:

The grand total is 2.60 + 3.00 + 3.40 = 9.00 kg and the grand mean is 9.00 ÷ 12 = 0.75 kg/day.

Sum of squares between groups = 4 × (0.65 − 0.75)² + 4 × (0.75 − 0.75)² + 4 × (0.85 − 0.75)² = 4 × 0.01 + 0 + 4 × 0.01 = 0.08

Sum of squares within groups = 0.005 + 0.005 + 0.005 = 0.015, because in each ration the squared differences from the ration mean are 0.0025, 0, 0.0025 and 0.

Degrees of freedom: between groups 3 − 1 = 2; within groups 12 − 3 = 9.

Mean square between = 0.08 ÷ 2 = 0.04

Mean square within = 0.015 ÷ 9 = 0.001667

F = 0.04 ÷ 0.001667 = 24.0

The critical value of F for 2 and 9 degrees of freedom at the 5% level is 4.26. Since 24.0 is larger than 4.26, the null hypothesis is rejected: at least one ration gives a different weight gain. ANOVA shows that a difference exists but not which rations differ; a follow-up comparison of pairs is needed for that.

3.1.2 Measures of central tendency

A measure of central tendency gives one value that represents the centre of a set of observations. It lets a researcher describe the typical performance of a herd, such as the usual daily milk yield, without listing every animal. The choice of measure depends on the data type and on whether extreme values are present.

Mean

The mean is the sum of all observations divided by their number. It uses every value, which makes it the standard measure for symmetric data, but a few extreme values pull it away from the centre.

Median

The median is the middle value when the observations are arranged in order; with an even number of observations it is the average of the two middle values. Extreme values hardly affect it, so it describes skewed data better than the mean.

Mode

The mode is the value that occurs most often. It is the only one of the three that suits categories, such as the breed that appears most often in a herd, and a set of data may have more than one mode.

Geometric mean

The geometric mean is the nth root of the product of n values. It is used for growth rates and ratios that multiply from one period to the next. Example: if milk yield rose by a factor of 1.2 in the first year and 1.3 in the second, the average yearly factor is √(1.2 × 1.3) = √1.56 = 1.249, an increase of about 24.9% a year.

Harmonic mean

The harmonic mean is the number of values divided by the sum of their reciprocals. It is used to average rates when the same amount of work is done at each rate. Example: two milkers each milk 20 cows, one at 10 cows an hour and the other at 5 cows an hour. The average rate is 2 ÷ (1/10 + 1/5) = 2 ÷ 0.3 = 6.67 cows an hour, which agrees with 40 cows in 2 + 4 = 6 hours.

Worked example

The daily milk yields of seven cows in litres are 12, 14, 15, 15, 16, 18 and 30.

Mean = (12 + 14 + 15 + 15 + 16 + 18 + 30) ÷ 7 = 120 ÷ 7 = 17.14 litres

Median: the ordered values are the same list, and the fourth of seven values is 15 litres.

Mode: 15 litres occurs twice and every other value once.

The one very high yield of 30 litres raises the mean above the median and mode. For this herd, 15 litres describes a typical cow better than 17.14 litres.

3.1.3 Measures of dispersion

Measures of dispersion show how widely observations spread around the centre. Two herds can have the same mean milk yield while one is uniform and the other very uneven, and the uneven herd is harder to feed and manage. Dispersion also tells a researcher how far a mean can be trusted.

Range

The range is the largest value minus the smallest. It is quick to find but uses only two observations, so one extreme value changes it greatly.

Variance

The variance is the average of the squared differences between each observation and the mean. For a sample, the sum of squared differences is divided by n − 1, not n. The units are squared, such as kg², which makes the variance hard to picture.

Standard deviation

The standard deviation is the square root of the variance and is in the same units as the data. A small standard deviation means the animals are close to the mean; a large one means they are spread out.

Coefficient of variation

The coefficient of variation is the standard deviation divided by the mean, multiplied by 100 and expressed as a percentage. Because it has no units, it compares the spread of measurements with different units or very different means, such as milk yield in litres against body weight in kilograms.

Interquartile range

The interquartile range is the third quartile minus the first quartile and covers the middle half of the ordered data. Extreme values have little effect on it, so it suits skewed data and is paired with the median.

Worked example

The birth weights in kilograms of six dairy calves are 28, 30, 32, 32, 34 and 36.

Mean = (28 + 30 + 32 + 32 + 34 + 36) ÷ 6 = 192 ÷ 6 = 32 kg

Range = 36 − 28 = 8 kg

Differences from the mean: −4, −2, 0, 0, 2, 4. Squared: 16, 4, 0, 0, 4, 16. Sum = 40.

Sample variance = 40 ÷ (6 − 1) = 8 kg²

Standard deviation = √8 = 2.83 kg

Coefficient of variation = 2.83 ÷ 32 × 100 = 8.84%

Interquartile range: the lower half is 28, 30, 32, so Q1 = 30; the upper half is 32, 34, 36, so Q3 = 34; IQR = 34 − 30 = 4 kg.

Most calves in this group weigh within 2.83 kg of the mean, and the middle half of the calves differ by only 4 kg.

Chapter Summary

This chapter focused on analyzing scientific research findings by first identifying key data analysis results that emerge from collected information. It detailed the process of performing data analysis, emphasizing techniques and tools necessary to transform raw data into meaningful patterns and conclusions. The chapter then covered the preparation of a research report, highlighting how to effectively present findings in a structured and coherent manner. Attention was given to ensuring clarity, accuracy, and relevance in the report to communicate the research outcomes convincingly. Throughout, the importance of critical evaluation and systematic organization was underscored to support valid scientific conclusions. This comprehensive approach equips students with the skills needed to interpret data and share their research insights professionally.