3.1 Research findings

Research findings represent the results derived from systematic investigations aimed at answering specific questions or testing hypotheses. In horticulture, these findings could relate to plant growth patterns, effects of fertilisers, pest resistance, or climate impacts on crop yields. Understanding and interpreting research findings allows horticulturists to apply scientific knowledge practically, improving productivity and sustainability in Kenya's diverse farming environments.

3.1.1 Definition of research findings

Research findings are the conclusive information obtained after collecting, processing, and analysing data during a research study. They reflect the outcomes of the research objectives and provide evidence to support or refute hypotheses. In horticulture, findings might show the effectiveness of a new irrigation technique or the impact of a pest control method on yield quality.

Characteristics of research findings

• Evidence-based: Research findings are grounded in data collected through rigorous methods, ensuring reliability and validity.
• Objective: Findings should be free from researcher bias, presenting an accurate representation of observed phenomena.
• Replicable: Properly documented findings allow other researchers to reproduce the study under similar conditions.
• Context-specific: Findings often depend on environmental and socio-economic conditions, such as soil type or farming practices in Kenya.
• Actionable: Good research findings provide clear guidance for decision-making and practical application in horticulture.

Types of research findings

• Quantitative findings: Numerical data outcomes, such as yield increases or pest infestation rates.
• Qualitative findings: Descriptive insights, like farmer perceptions of crop varieties or challenges in pest management.
• Mixed-method findings: Combination of quantitative and qualitative results providing a comprehensive understanding.
• Confirmatory findings: Evidence that supports a hypothesis or theory.
• Exploratory findings: New observations that generate hypotheses for further research.

Importance of research findings in horticulture

• Improved crop management: Findings help optimise fertiliser use, irrigation schedules, and pest control.
• Enhanced productivity: Evidence-based practices increase yields and quality of horticultural crops.
• Sustainability: Findings inform environmentally friendly practices, such as organic farming or water conservation.
• Policy formulation: Research outcomes guide governmental and institutional policies on agriculture and food security.
• Capacity building: Findings contribute to training extension officers and farmers on best practices.

Challenges in interpreting research findings

• Complex data: Advanced statistical results may be difficult for practitioners without training to understand.
• Context variability: Findings from one region may not apply directly to another due to differing climate or soil.
• Publication bias: Positive results are often published more, skewing the available evidence.
• Misinterpretation: Without proper analysis, findings can be misunderstood, leading to incorrect application.
• Resource constraints: Limited access to full research reports or databases can hinder thorough review.

3.1.2 Identify data analysis methods

Raw data from a field or greenhouse trial, such as plot yields, plant heights or pest counts, say very little until they are summarised and tested. Data analysis methods turn the measurements into numbers that describe the typical result, show how much the results vary, and test whether differences between treatments are real or just chance. In a horticultural trial comparing fertiliser types on tomatoes, the researcher uses measures of central tendency and dispersion to describe each treatment and ANOVA to compare them.

3.1.2.1 ANOVA

ANOVA (Analysis of Variance) is a statistical test used to decide whether the means of three or more groups differ by more than chance alone would explain. It does this by comparing the variation between the treatment means with the variation within the treatments. In horticulture it is the standard tool for replicated trials, for example comparing the yield of tomatoes grown with no fertiliser, NPK fertiliser and compost. Running separate comparisons between pairs of treatments increases the risk of false positives, which is why ANOVA is used first.

Hypotheses and test statistic: the null hypothesis (H0) states that all treatment means are equal. The alternative hypothesis (H1) states that at least one treatment mean is different. The test statistic is the F ratio:

F = Mean square between treatments ÷ Mean square within treatments

A large F value means the differences between treatments are large compared with the natural variation among replicates.

Assumptions of ANOVA:

• Independence: Each plot or plant is measured separately, and one plot's result does not influence another.
• Random allocation: Treatments are assigned to plots by chance, for example in a randomised complete block design, to avoid bias from soil or slope.
• Normality: The residuals (differences from the treatment mean) are approximately normally distributed.
• Equal variances: The spread of values is similar in all treatments.
• Continuous data: The measured variable, such as yield in kg or height in cm, is numerical.

Steps in a one-way ANOVA. Worked example: a trial compares tomato yield (kg per plot) under three treatments, each replicated on four plots.

1. State the hypotheses. H0: the mean yields of A, B and C are equal. H1: at least one mean yield differs.

2. Calculate the grand total and the correction factor (CF). The number of observations is N = 12.

   • Grand total = 52 + 68 + 64 = 184 kg
   • CF = (grand total)² ÷ N
   • CF = 184² ÷ 12 = 33 856 ÷ 12 = 2821.33

3. Calculate the total sum of squares (SST), which measures all the variation in the data. The sum of the squares of all 12 values is 678 + 1158 + 1026 = 2862.

   • SST = Σx² − CF
   • SST = 2862 − 2821.33 = 40.67

4. Calculate the between-treatment sum of squares (SSB), which measures variation caused by the treatments. Each treatment has r = 4 plots.

   • SSB = (ΣT²) ÷ r − CF
   • SSB = (52² + 68² + 64²) ÷ 4 − 2821.33
   • SSB = (2704 + 4624 + 4096) ÷ 4 − 2821.33 = 2856 − 2821.33 = 34.67

5. Calculate the within-treatment (error) sum of squares (SSW), which measures the natural variation among replicates.

   • SSW = SST − SSB
   • SSW = 40.67 − 34.67 = 6.00

6. Find the degrees of freedom (df) and the mean squares.

   • df between = number of treatments − 1 = 3 − 1 = 2
   • df within = N − number of treatments = 12 − 3 = 9
   • Mean square between = 34.67 ÷ 2 = 17.33
   • Mean square within = 6.00 ÷ 9 = 0.667

7. Calculate F and compare it with the critical value from F tables.

   • F = 17.33 ÷ 0.667 = 26.0
   • The critical F value for 2 and 9 degrees of freedom at the 5% level is 4.26

8. Decide and interpret. Since 26.0 is greater than 4.26, H0 is rejected: at least one treatment mean differs significantly.

Interpreting ANOVA results: a significant F only shows that the treatments are not all equal; it does not say which ones differ. A follow-up (post hoc) test such as Tukey's test or the least significant difference (LSD) is then used to compare treatment means in pairs. In the example, the means of 13, 17 and 16 kg per plot would be compared to show whether NPK and compost both exceed the control and whether they differ from each other. The researcher reports the F value, the degrees of freedom and the significance level, together with the treatment means.

3.1.2.2 Measures of central tendency

A measure of central tendency is a single value that represents the centre or typical value of a data set. The three main measures are the mean, the median and the mode. Horticulturists use them to summarise results, for example the average plant height in a treatment, so that treatments can be compared and reported simply.

The worked data below are the heights (cm) of nine French bean plants measured four weeks after planting: 22, 24, 25, 25, 26, 27, 28, 29, 34.

Mean: the mean is the sum of all values divided by the number of values. It uses every observation and is the basis of most statistical tests, including ANOVA.

• Mean = Σx ÷ n
• Mean = (22 + 24 + 25 + 25 + 26 + 27 + 28 + 29 + 34) ÷ 9
• Mean = 240 ÷ 9 = 26.67 cm

Median: the median is the middle value when the data are arranged in order. For an odd number of values it is the middle one; for an even number it is the average of the two middle values.

• Position of the median = (n + 1) ÷ 2 = (9 + 1) ÷ 2 = 5th value
• Median = 26 cm

Mode: the mode is the value that occurs most often. A data set may have one mode, more than one, or none.

• In the bean data, 25 appears twice and every other value once
• Mode = 25 cm

Choosing the right measure:

• Mean: Best for evenly spread numerical data, such as yield per plot. It is affected by extreme values: the one tall plant of 34 cm pulls the mean (26.67 cm) above the median (26 cm).
• Median: Best for skewed data or data with outliers, such as the number of insects per plant, where a few plants carry very high counts.
• Mode: Best for the most frequent category or size, such as the most common grade of harvested fruit.
• Reporting: The mean is normally reported together with a measure of dispersion, because the mean alone hides how variable the plants were.
• Checking: When the mean, median and mode are close together, the data are roughly symmetrical.

3.1.2.3 Measures of dispersion

A measure of dispersion shows how widely the values in a data set are spread around the centre. Two treatments can have the same mean yield but very different reliability: one gives uniform plots, while the other gives some very high and some very poor plots. Measures of dispersion let the researcher judge the consistency of a crop practice and are needed for ANOVA and other tests.

The same French bean heights (cm) are used: 22, 24, 25, 25, 26, 27, 28, 29, 34, with a mean of 26.67 cm and n = 9.

Range: the range is the difference between the largest and smallest values. It is simple but depends only on the two extreme values.

• Range = maximum − minimum
• Range = 34 − 22 = 12 cm

Interquartile range: the interquartile range (IQR) is the spread of the middle half of the data, so it is not affected by extreme values. The data are split at the median, and the median of the lower half gives the first quartile (Q1) and of the upper half the third quartile (Q3).

• Lower half: 22, 24, 25, 25, so Q1 = (24 + 25) ÷ 2 = 24.5 cm
• Upper half: 27, 28, 29, 34, so Q3 = (28 + 29) ÷ 2 = 28.5 cm
• IQR = Q3 − Q1 = 28.5 − 24.5 = 4 cm

Variance: the variance is the average squared deviation from the mean. For a sample, the sum of squared deviations is divided by n − 1.

• Variance (s²) = Σ(x − mean)² ÷ (n − 1)
• Σ(x − mean)² = Σx² − (Σx)² ÷ n = 6496 − 240² ÷ 9 = 6496 − 6400 = 96
• s² = 96 ÷ (9 − 1) = 12.0 cm²

Standard deviation: the standard deviation is the square root of the variance. It is in the same units as the data, so it is easier to interpret than the variance.

• s = √variance
• s = √12.0 = 3.46 cm

A small standard deviation means the plants were similar in height; a large one means the heights varied widely.

Standard error of the mean: the standard error shows how precisely the sample mean estimates the true mean. It is commonly shown as error bars on graphs of treatment means.

• SE = s ÷ √n
• SE = 3.4641 ÷ √9 = 3.4641 ÷ 3 = 1.15 cm

Coefficient of variation: the coefficient of variation (CV) expresses the standard deviation as a percentage of the mean. It allows variability to be compared between data sets with different units or sizes, such as plant height and fruit mass.

• CV = (s ÷ mean) × 100
• CV = (3.4641 ÷ 26.6667) × 100 = 13.0%

Chapter Summary

This chapter focused on understanding research findings by first defining what research findings entail as the outcomes derived from systematic investigation. It then explored various data analysis methods critical for interpreting research data, including ANOVA, which compares means across multiple groups, measures of central tendency that summarize data through averages or medians, and measures of dispersal that describe the spread or variability within data sets. The chapter further guided students through performing data analysis, emphasizing the practical application of these methods to extract meaningful insights from collected data. Finally, it addressed the preparation of a research report, highlighting the importance of effectively communicating analyzed results in a structured and coherent manner suitable for academic and professional audiences.