Analyzing scientific research findings is a crucial skill for Food and Beverage Management professionals in Kenya, enabling them to make informed decisions backed by evidence. This chapter equips learners with the knowledge to interpret research data accurately, prepare comprehensive research reports, and uphold ethical standards in reporting. Mastery of these skills ensures that managers and practitioners can apply research outcomes to improve service quality, customer satisfaction, and operational efficiency in diverse hospitality settings.

3.1 Data analysis methods

Data analysis is the process of organising, summarising and interpreting the data collected in a study so that it answers the research questions and tests the hypotheses. Raw questionnaire scores, sales figures or waiting times mean little until they are reduced to a few figures that describe the typical value and the spread, and until groups are compared with a suitable statistical test. Measures of central tendency and measures of dispersion describe a set of data, while tests such as ANOVA allow the researcher to decide whether differences between groups are real or due to chance. Example: a food and beverage manager at a lakeside hotel in Bondo summarises a month of guest ratings with a mean and standard deviation, then compares the ratings of breakfast, lunch and dinner service.

ANOVA

ANOVA (Analysis of Variance) is a statistical test that compares the means of three or more groups to determine whether at least one group mean differs significantly from the others. Comparing many groups two at a time with separate t-tests raises the chance of a false conclusion, so ANOVA tests all the groups at once. It works by comparing the variation between the group means with the variation within the groups: if the groups differ much more from each other than their members differ among themselves, the difference is unlikely to be due to chance.

Uses of ANOVA in food and beverage research

• Comparing outlets: Whether guest satisfaction differs between three or more restaurants of a group.
• Comparing recipes: Whether taste panel scores differ between several versions of a dish.
• Comparing shifts: Whether average order-to-table time differs between breakfast, lunch and dinner service.
• Comparing training methods: Whether staff trained by different methods differ in upselling results.
• Comparing guest groups: Whether average spend differs between business, leisure and conference guests.

Key terms in ANOVA

• Null hypothesis (H0): All group means are equal.
• Alternative hypothesis (H1): At least one group mean is different.
• Sum of squares between groups (SSB): Variation of the group means around the grand mean.
• Sum of squares within groups (SSW): Variation of individual scores around their own group mean.
• Degrees of freedom (df): Between groups = k − 1; within groups = N − k, where k is the number of groups and N the total number of scores.
• Mean square (MS): A sum of squares divided by its degrees of freedom.
• F ratio: F = MSB ÷ MSW. A large F suggests real differences between groups.
• Significance level: Usually 0.05; if the calculated F is greater than the critical F from tables (or the p-value is below 0.05), H0 is rejected.

Assumptions of ANOVA

• Independence: Each score comes from a different, independent respondent or unit.
• Normality: Scores in each group are roughly normally distributed.
• Equal variances: The spread of scores is similar in each group.
• Interval or ratio data: The dependent variable is measured on a numerical scale, such as a rating out of 10 or time in minutes.

Worked example: one-way ANOVA

A college in Kangundo runs three cafeterias. Three students from each rate the meal on a scale of 1 to 10. Is there a significant difference in mean rating at the 0.05 level?

Step 1: Grand mean

Grand mean = sum of all scores ÷ N

Grand mean = (21 + 18 + 27) ÷ 9

Grand mean = 66 ÷ 9 = 7.333

Step 2: Sum of squares between groups

SSB = Σ n × (group mean − grand mean)²

SSB = 3 × (7 − 7.333)² + 3 × (6 − 7.333)² + 3 × (9 − 7.333)²

SSB = 3 × 0.111 + 3 × 1.778 + 3 × 2.778 = 0.333 + 5.333 + 8.333

SSB = 14.0

Step 3: Sum of squares within groups

SSW = Σ (score − own group mean)²

Cafeteria A = (6 − 7)² + (7 − 7)² + (8 − 7)² = 1 + 0 + 1 = 2

Cafeteria B = (5 − 6)² + (6 − 6)² + (7 − 6)² = 1 + 0 + 1 = 2

Cafeteria C = (8 − 9)² + (9 − 9)² + (10 − 9)² = 1 + 0 + 1 = 2

SSW = 2 + 2 + 2 = 6.0

Step 4: Degrees of freedom

df between = k − 1 = 3 − 1 = 2

df within = N − k = 9 − 3 = 6

Step 5: Mean squares and F ratio

MSB = SSB ÷ df between = 14.0 ÷ 2 = 7.0

MSW = SSW ÷ df within = 6.0 ÷ 6 = 1.0

F = MSB ÷ MSW = 7.0 ÷ 1.0 = 7.0

Step 6: Decision

The critical value of F for 2 and 6 degrees of freedom at the 0.05 level is 5.14 (from F tables). The calculated F of 7.0 is greater than 5.14 (p is about 0.027), so H0 is rejected: the mean ratings of the three cafeterias differ significantly. ANOVA shows only that a difference exists; a follow-up (post hoc) test such as Tukey's test shows which pairs differ, here most likely Cafeteria C against A and B.

Measures of central tendency

Measures of central tendency are single values that represent the centre or typical value of a set of data. They summarise many scores in one figure that is easy to report and compare, such as the average spend per guest or the most popular dish. The three measures are the mean, the median and the mode, and the right one depends on the type of data and on whether it contains extreme values.

The examples below use one data set: the waiting times, in minutes, of eight orders at a fish restaurant in Ahero: 12, 15, 10, 18, 15, 20, 15, 11.

Mean

The mean (arithmetic average) is the sum of all values divided by the number of values. It uses every value in the data, which makes it the most widely used measure and the basis of variance, standard deviation and ANOVA. Its weakness is that extreme values pull it up or down.

Ungrouped data:

Mean = Σx ÷ n

Mean = (12 + 15 + 10 + 18 + 15 + 20 + 15 + 11) ÷ 8

Mean = 116 ÷ 8

Mean = 14.5 minutes

Data in a frequency table (guest ratings of a dessert on a 1 to 5 scale):

Mean = Σfx ÷ Σf

Mean = 67 ÷ 20

Mean = 3.35

Grouped data (spend per guest at a hotel bar, using class midpoints):

Mean = Σfx ÷ Σf

Mean = 40,750 ÷ 35

Mean = Ksh 1,164.29

Median

The median is the middle value when the data is arranged in order from smallest to largest. Half the values lie below it and half above. It is not affected by extreme values, so it is preferred for skewed data such as guest bills, incomes or prices.

Even number of values: arrange the waiting times in order: 10, 11, 12, 15, 15, 15, 18, 20.

Position of median = (n + 1) ÷ 2 = (8 + 1) ÷ 2 = 4.5th value

Median = (4th value + 5th value) ÷ 2 = (15 + 15) ÷ 2

Median = 15 minutes

Odd number of values: five guest bills of Ksh 850, 1,200, 640, 2,300 and 980, in order: 640, 850, 980, 1,200, 2,300.

Position of median = (5 + 1) ÷ 2 = 3rd value

Median = Ksh 980

The mean of these bills is 5,970 ÷ 5 = Ksh 1,194, pulled up by the single large bill of Ksh 2,300, while the median of Ksh 980 better represents a typical guest.

Frequency table: in the dessert ratings above, n = 20, so the median lies between the 10th and 11th values. The cumulative frequencies are 2, 5, 10, 16, 20, so the 10th value is 3 and the 11th is 4.

Median = (3 + 4) ÷ 2 = 3.5

Grouped data: in the bar spend table, n ÷ 2 = 35 ÷ 2 = 17.5. The cumulative frequencies are 4, 14, 26, 32, 35, so the 17.5th value lies in the class 1,000 to under 1,500.

Median = L + ((n ÷ 2 − CF) ÷ f) × h

where L = lower boundary of the median class (1,000), CF = cumulative frequency before it (14), f = frequency of the median class (12), h = class width (500)

Median = 1,000 + ((17.5 − 14) ÷ 12) × 500

Median = 1,000 + 0.2917 × 500 = 1,000 + 145.83

Median = Ksh 1,145.83

Mode

The mode is the value that occurs most often in a data set. It is the only measure that can be used for categorical data, such as the most ordered dish, the most common complaint or the most popular payment method. A data set may have one mode (unimodal), two modes (bimodal), several modes or none.

Waiting times: 10, 11, 12, 15, 15, 15, 18, 20. The value 15 occurs three times, more than any other.

Mode = 15 minutes

Dessert ratings: the highest frequency is 6, for a rating of 4.

Mode = 4

Grouped data: the modal class is the class with the highest frequency, 1,000 to under 1,500 (f = 12).

Mode = L + ((f1 − f0) ÷ ((f1 − f0) + (f1 − f2))) × h

where L = 1,000, f1 = frequency of the modal class (12), f0 = frequency of the class before (10), f2 = frequency of the class after (6), h = 500

Mode = 1,000 + ((12 − 10) ÷ ((12 − 10) + (12 − 6))) × 500

Mode = 1,000 + (2 ÷ 8) × 500 = 1,000 + 125

Mode = Ksh 1,125

Choosing the measure of central tendency

Measures of dispersion

Measures of dispersion show how spread out the values in a data set are around the centre. Two outlets may have the same mean waiting time of 15 minutes, but if one ranges from 14 to 16 minutes and the other from 5 to 30 minutes, guests at the second have a very unpredictable experience. Dispersion therefore measures consistency, which is central to quality in food and beverage service. The main measures are the range, the variance and the standard deviation.

Range

The range is the difference between the largest and smallest values. It is the simplest measure of spread and quick to calculate, but it uses only two values and is distorted by a single extreme value.

Range = highest value − lowest value

Range = 20 − 10

Range = 10 minutes

Variance

The variance is the average of the squared deviations of each value from the mean. Squaring removes negative signs and gives more weight to values far from the mean. For a sample, the sum of squared deviations is divided by n − 1; for a whole population it is divided by N. Variance is expressed in squared units, which makes it hard to interpret directly, but it is the basis of the standard deviation and of ANOVA.

Sample variance: s² = Σ(x − mean)² ÷ (n − 1)

Using the waiting times, with mean = 14.5:

s² = 82 ÷ (8 − 1)

s² = 82 ÷ 7

s² = 11.71 minutes²

If the eight orders were the whole population, the population variance would be 82 ÷ 8 = 10.25 minutes².

Standard deviation

The standard deviation is the square root of the variance. It is expressed in the same units as the data, so it shows directly how far, on average, values lie from the mean. A small standard deviation means consistent performance; a large one means wide variation. In roughly normal data, about 68 per cent of values lie within one standard deviation of the mean and about 95 per cent within two.

s = √s²

s = √11.71

s = 3.42 minutes

Interpretation: orders at the restaurant take a mean of 14.5 minutes, and most orders arrive within about 3.4 minutes either side of this, that is between about 11.1 and 17.9 minutes. (The population standard deviation would be √10.25 = 3.20 minutes.)

Comparing consistency: if a second outlet also has a mean of 14.5 minutes but a standard deviation of 7.8 minutes, its service is far less consistent, even though the average is the same.

Other quantitative analysis techniques

• Frequencies and percentages: Count how many respondents chose each answer, such as 64 per cent rating the food as good.
• Cross-tabulation: Shows how answers differ between groups, such as satisfaction by age group.
• t-test: Compares the means of two groups, such as weekday and weekend spend.
• Chi-square test: Tests whether two categorical variables are related, such as gender and choice of beverage.
• Correlation and regression: Measure the relationship between variables and predict one from another, such as forecasting covers from room occupancy.

Qualitative data analysis

Qualitative data from interviews, focus groups, suggestion boxes and open-ended questions is analysed by reading, coding and grouping it into themes rather than by calculation.

1. Transcribe: Write out recordings and notes in full.
2. Read and familiarise: Read all the data several times to get an overall picture.
3. Code: Label each meaningful phrase with a short code, such as "slow service" or "portion size".
4. Group into themes: Combine related codes into broader themes, such as "service speed" or "value for money".
5. Review and define themes: Check that each theme is supported by the data and name it clearly.

6. Report: Present each theme with short, anonymous quotations as evidence.

7. Content analysis: Counts how often codes or words occur, such as how many comment cards mention cleanliness.

8. Thematic analysis: Identifies patterns of meaning across the data.
9. Narrative analysis: Examines the stories participants tell about their experiences.

Use of statistical software in data analysis

Software makes analysis faster and more accurate, especially with large data sets, and produces tables and charts ready for the research report.

• Microsoft Excel: Calculates means, medians, standard deviations and simple charts; widely available to small food businesses.
• SPSS: User-friendly package for descriptive statistics, t-tests, ANOVA, chi-square and regression, popular for questionnaire data.
• Stata and R: Used for advanced statistical and econometric analysis; R is free.
• NVivo and Atlas.ti: Help organise and code qualitative data from interviews and focus groups.
• Online survey tools: Collect questionnaire responses electronically and give basic summaries automatically.

Example: a researcher at an agricultural training centre in Kimilili enters 300 questionnaires into SPSS and produces a table of mean ratings and standard deviations for each department in under an hour.

Chapter Summary

This chapter explored various data analysis methods essential for interpreting research findings accurately, emphasizing their role in deriving meaningful conclusions. It then examined the structure and key components of research reports, highlighting how each section contributes to clear and coherent communication of the study. The design of research reports was discussed, focusing on organizing content logically to facilitate reader understanding and engagement. Ethical considerations in research were addressed, underscoring the importance of integrity, confidentiality, and respect for participants throughout the research process. The chapter concluded with guidance on proper citation and referencing practices, which are critical for acknowledging sources and avoiding plagiarism. Together, these topics provide a comprehensive framework for analyzing and presenting scientific research effectively in the hospitality field.