A diagram showing the six steps of research, arranged in a cycle: Ask, Design, Collect, Classify and summarise, Analyse, Report. Step 1 (Ask) is highlighted, captioned “Ask the RQ”.
The research question (RQ) directs all other components of the research. Since quantitative research summarises and analyses data using numerical methods (like averages or percentages), the RQ must be written carefully so it can be answered effectively. Four different types of RQs are studied:
Since the RQ directs all other components of the research, writing RQs should be the first step of any research study. Specifically, RQs should be asked before data are collected.
Data are rarely taken from all the individuals in the population: all individuals are rarely accessible in practice. For example, testing a new drug cannot possibly study all people who might use the drug (some may not even be born yet). In contrast, a sample is a subset of the population from which data are obtained (Chapter 6). Countless samples are possible from any given population, but only one is studied.
The study compared \(28\) active and \(28\) sedentary American college women, from which data were collected. The population was all active and sedentary American college women. The group of \(56\) subjects was the sample.
Descriptive RQs study something about the identified population, called the outcome. Because the RQ concerns a large group (the population), the outcome numerically describes a group of individuals (not single individuals). The outcome is, for example, an average or proportion summarising a group of individuals.
Some RQs ask about the value of some population quantity (such as: what is the average internal body temperature?); these are called estimation RQs. Some RQs require making a decision about the population (such as: is the average internal body temperature the same for females and males?); these are called decision-making RQs. Descriptive RQs have one of these forms, depending on what information is sought (Section 2.8):
Answering estimation descriptive RQs is studied in Chapter 22 and Chapter 23. Answering decision-making descriptive RQs is studied in Chapter 26 and Chapter 27.
[34] studied men and women aged \(18\) to \(40\text{;}\) this is the population. The outcome of interest in this population is the average body temperature. The sample comprised \(148\) “healthy men and women” aged \(18\) to \(40\text{.}\) One descriptive RQ was:
This is an estimation RQ. They also studied a decision-making descriptive RQ (where \(98.6^{\circ}\text{F}\) (or \(37.0^{\circ}\text{C}\)) is a commonly-accepted value for the internal body temperature):
Studying relationships usually is more interesting than simply describing a population. Relational RQs compare the outcome for groups of different individuals in the population, or compare two different sub-populations. These comparisons are called between-individuals comparisons, as they compare the outcome between (or among) groups of different individuals. Examples include:
comparing the average heart rate across three groups of people: those not receiving the drug, those receiving a weekly dose, and those receiving a daily dose of the drug.
[29] compared the average weight of female and male Leadbeater’s possums. “Sex of the possum” is the between-individuals comparison; average weight is the outcome.
The population is “Cubans \(13\) and \(20\) years of age”, the outcome is “average heart rate”, and the between-individuals comparison is between two separate groups: “between females and males”. This is a relational RQ.
This is a decision-making RQ, since it asks if the average heart rate is the same for females and males. An estimation-type relational RQ would ask about the size of difference in the average heart rate between females and males.
Rather than comparing the outcome for groups of different individuals, repeated-measures RQs compare the outcome multiple times within the same individuals.
These comparisons are called within-individuals comparisons, as they compare the outcome within the same individuals, not across groups of different individuals. The multiple measurements may be different points in time (e.g., the height of the same trees at one, two and five years after planting), but do not have to be time points.
The within-individuals comparison in the RQ identifies the small number of different, distinct situations for which the outcome is compared for each individual.
A between-individuals comparison would compare the average strengths of the dominant and non-dominant legs between different groups of footballers: one group would have their dominant-leg strength measured, and the other would have their non-dominant-leg strength measured. This is a between-individuals comparison.
In contrast, the strengths of the dominant and non-dominant legs could be recorded on the same individuals. This study examines within-individuals changes: the average differences between the strengths of the dominant and non-dominant legs within the same individuals. In this study, no between-individuals comparison exists: different groups are not being compared.
Studies may use both within- and between-individuals comparisons (see Section 30.8). For instance, a study may examine the change in individuals’ heart rate (the within-individuals comparison), for two drugs given to different groups (the between-groups comparison).
The comparison is within individuals, as the temperature is measured for the same tree hollows at the two times. This is a repeated-measures, estimation-type RQ.
[60] compared the weights of the same university students at the beginning of university, and then after \(12\) weeks. The comparison is within individuals, and the study is a repeated-measures study. Since each student has a pair of weight measurements, this is a paired study.
RQs are about populations. However, the data to answer an RQ come from individuals in that population. The aspects or characteristics that can vary are called variables.
Examples of variables include: the duration of cold symptoms; sex; tree girth; response to a survey question (Yes, Maybe, No); city of birth; hair colour.
Some variables change from one individual to another individual, such as sex and height. These are called between-individuals variables. In repeated-measures studies, some variables of interest change over repeated measurements from the same individuals; these are called within-individuals variables.
Definition2.23.Between- and within-individuals variables.
Between-individuals variables vary from one individual to another individual. Within-individuals variables vary from one recording or measurement to another within the same individuals.
A between-individuals variable is a single aspect that can vary from individual to individual. While your city of birth does not change, “city of birth” is a variable because it varies from individual to individual.
[74] compared the temperature in the same tree hollows in summer and winter (Example 2.19). The comparison is within individuals: the temperature is measured for the same tree hollows (the individuals) at two different times.
“Season” is a within-individuals variable, as each tree hollow is studied for two different seasons. “Temperature” is also a within-individuals variable, as it is measured twice for each tree hollow.
“Sex of the possum” is a between-individuals variable; it can vary from possum to possum. “Weight” is also a between-individuals variable; it can vary from possum to possum.
“Duration of cold symptoms” is a between-individuals variable: its value can vary from individual to individual. The “average duration of cold symptoms” is the outcome, a numerical summary of many individuals’ cold durations.
Usually, one variable can be considered as perhaps influencing the value of the other variable. This variable is called the explanatory variable (which may explain changes in the other variable). The other is the response variable (whose values respond to changes in the explanatory variable). To be able to influence the response variable, the explanatory variable must occur before (or at the same time) as the response variable.
The value of the response variable may change in response to the value of the explanatory variable. The value of the explanatory variable may explain changes in the value of the response variable.
The response variable is sometimes called the dependent variable, and the explanatory variable is sometimes called the independent variable. We avoid these terms, since the words “dependent” and “independent” have many meanings in research.
The RQ cannot be answered without data for the response and explanatory variables. The outcome is a numerical summary of the values of the response variable (Table 2.32) recorded from many individuals. The values of the explanatory variable distinguish between the values of the comparison for the individuals (Table 2.33 and Table 2.34) being made.
The population comprises all public playgrounds in Boston; each public playground is an individual. The outcome is the average ground surface temperature in summer over many playgrounds; the response variable is the ground surface temperature for individual ground surfaces in summer.
The between-individuals comparison is between the four types of ground surfaces (rubber, soil, sand, mulch). The explanatory variable is the type of surface for individual playgrounds.
Correlational RQs are not concerned with summarising outcomes in comparison groups. Instead, correlational RQs explore relationships between two variables measured or observed on or about the individuals.
Usually, one variable can be considered as the explanatory variable, and the other as the response variable (Section 2.5). To be able to influence the response variable, the explanatory variable must occur before (or at the same time) as the response variable. Explanatory and response variables may be either within- or between-individuals variables.
Consider studying marathon runners. An RQ exploring the relationship between the individuals’ water intake on the day before the race and the individuals’ race times would be a correlational RQ. The water intake on the day before the race may influence the race time.
One correlational RQ concerned the relationship between the diameter of trees at breast height (DBH; response variable), and the pH of the soil (explanatory variable). The two variables are the DBH and pH, both recorded for many trees.
Also studied was the relationship between the DBH for each tree at various times after the planting date (a repeated-measure RQ). Each tree has the DBH measured over time, for many time points. Time is the within-individuals comparison.
[47] recorded the length and weight of \(14\,040\) fish for \(39\) demersal fish species. The study has two variables (fish length; fish weight), but identifying a response variable and explanatory variable is meaningless. The estimation-type correlational RQ is:
Sometimes, the explanatory variable naturally occurs without manipulation by the researchers (e.g., the height of people; the sex of oxen; the pH of forest soil). Sometimes, however, the explanatory variable is manipulated by researchers (e.g., the dose of fertiliser applied; the dose of drug given); this is called an intervention.
An intervention is present when researchers can manipulate (or impose) the values of the explanatory variable on the individuals to determine the impact on the response variable.
When an intervention is present, the values of the explanatory variable are manipulated by the researchers, and are called treatments. When an intervention is not present, the values of the explanatory variable are not manipulated by the researchers, and are called conditions. The analysis is the same whether an intervention is used or not, but the interpretation of the results depend on whether an intervention is used (Section 4.5).
The conditions are the values of the explanatory variable that those in the study have or experience, but are not manipulated or imposed by the researchers.
[15]supplied one group of participants with a diet using refined flour, and supplied another group of participants with a diet using a new flour variety. “Type of diet” is the (between-individuals) explanatory variable. Since the researchers manipulate which subjects ate which flour, this study has an intervention. “Type of diet” is the treatment.
To compare the average blood pressure in female and male Scots, blood pressure was measured using a blood pressure machine (a sphygmomanometer). The researchers interact with the participants to measure blood pressure, but there is no intervention. Using the sphygmomanometer is just a way to measure blood pressure, to obtain the data.
The comparison is between females and males (the conditions), which cannot be manipulated or imposed on the individuals by the researchers; there is no intervention.
Often, one of the comparison groups is the control group. The control group is a comparison group not receiving the treatment being studied, or not having the condition being studied, but as similar as possible to the other individuals in all other ways. The control group is like a benchmark for detecting changes in the outcome due to the treatment or condition of interest (Section 7.5). Sometimes the control group is given a placebo: a non-effective treatment that appears to be the real treatment.
A control is an individual without the treatment or condition of interest, but as similar as possible in every other way to other individuals. A control group is a group of controls.
To test the effectiveness of a new medication, patients report to a doctor to receive injections of the new drug. Patients assigned to the control group do not receive the drug. The controls should also report to a doctor and receive an injection (like those receiving the drug); the injection, however, would contain no active ingredients (a placebo).
Together, the Population, Outcome, Comparison and Intervention form the POCI acronym (sometimes written as PICO) to aid remembering the elements of RQs. The POCI acronym is not helpful for correlational RQs.
The outcome is the “average iron status”. The between-individuals comparison is between highly-active and sedentary women. For this comparison to be an intervention, the researchers would need to tell each individual woman to be highly active or sedentary. This seems unlikely, so the study does not have an intervention.
As noted earlier, RQs can be written with one of two purposes. Estimation RQs ask how precisely an unknown value in the population is estimated by the sample. Estimation RQs are answered using confidence intervals, which are discussed in Chapter 22 to Chapter 23, Chapter 29 to Chapter 31, plus Subsection 33.2.2 and Subsection 33.4.3.
Decision-making RQs have two possible answers. For the example above, the average zinc intake either is the same for boys and girls, or is not the same for boys and girls, in the population (Figure 2.50). These two options are hypotheses: potential answers to the RQ. However, answers are rarely clear in practice, since only one of the countless possible samples from the population is studied. Instead, researchers decide how strongly the sample evidence supports a particular hypothesis about the population.
Evidence may support or contradict a hypothesis; evidence rarely proves a hypothesis (at least, without any other support, such as theoretical support). Ultimately, after collecting data from a sample, a decision must be made about which explanation about the population is more consistent with the data collected.
A diagram showing a research question box on the left asking whether the average daily zinc intake is the same for boys and girls in British young people aged 4 to 18. Two hypothesis boxes on the right show YES (the average zinc intake is the same for boys and girls) and NO (the average zinc intake is not the same for boys and girls). A data box asks which the data supports.
The first two are two-tailed RQs (and are essentially asking the same question but in different ways): the average zinc intake could be higher for girls or higher for boys. We are just interested in whether any difference is present; that is, two options are being considered. The last two are one-tailed RQs, since they ask specifically about a difference in just one direction: boys lower than girls, or boys higher than girls.
Most RQs are two-tailed, unless a good reason exists to ask a one-tailed RQ before the data are collected (e.g., a drug has been developed specifically to reduce blood pressure). RQs should be formed before the data are collected.
To answer this question, the thickness of individual hair strands needs to be measured. The “things” from or about which measurements are taken are called units of observation.
For this RQ, the unit of observation is the hair strand: the thickness measurements are taken from the hair strands. Suppose the thickness of \(100\) hair strands is recorded. These \(100\) hair strands could be obtained in many different ways. Two options are to:
While each approach gives \(100\) measurements, these two approaches are very different. Only one man is represented in the first scenario, so every hair strand is likely to be similar. However, \(100\) different men are represented in the second. The difference is related to the concept of unit of analysis.
The purpose of the study is to make conclusions about “men”: the RQ is asking about “men”. Each different man provides a separate, independent measurement of hair strand thickness. The “man” is the unit of analysis; each man provides a unique example of a hair strand.
The first scenario above has one unit of analysis (which provided all \(100\) units of observation). The second scenario has \(100\) units of analysis (each providing one unit of observation).
The unit of analysis is the smallest collection of units of observations (and perhaps the units of observations themselves) about which conclusions are made; the smallest distinct elements of the population for which information is analysed.
In the hair-strand study, all the hair strands from the same man have essentially “lived their life together”: they are all washed together with the same shampoo, exposed to the same amount of sunlight and exercise, share the same genetics, etc. However, different men potentially use different shampoo, exercise differently, have different genetics, and so on. The hair of different men tends to exhibit distinct characteristics. Each man is a collection of units of observations (hair strands). This study has a sample size of just two: \(n = 2\text{.}\)
To compare the average amount of fibre in wholemeal and white bread, researchers take ten slices from one loaf of wholemeal bread, and ten slices from one loaf of white bread. The amount of fibre (in grams) in each slice is determined. The units of observation are the “slices”: the type of bread (explanatory variable) and the amount of fibre (response variable) are observed on individual slices.
The unit of analysis is the “loaf” (a collection of slices), because the RQ is comparing types of bread, and the slices for each type of bread are all from the same loaf. Slices from the same loaf share the same baker and bakery; they were made with the same ingredients, in the same oven, baked at the same temperature, etc.
The Spectrum website (accessed 18 Nov, 2022) reported a study where researchers examined “\(10\) neurons from each of the \(16\) mice” (November 2022). The researchers treated each neuron as an independent observation, so \(n = 16 \times 10 = 160\text{.}\)
However, neurons in the brain of the same animal are not independent observations. The unit of analysis is the mouse; the unit of observation is the neuron. The actual sample size was \(n = 16\text{;}\) each unit of analysis has \(10\) units of observation. A total of \(160\) neurons from \(16\) mice is very different to a study of \(160\) neurons from \(160\) genetically-different mice.
The units of observation and units of analysis may be the same, and often are the same. However, they are sometimes different, and identifying these situations is crucial. Importantly, studies compare units of analysis, not units of observation.
Suppose researchers record the diastolic blood pressure (DBP) from \(15\) patients aged under \(40\) years of age, and \(15\) different patients aged \(40\) or older. The DBP is measured on every patients’ right arm, so there are \(15\) observations for the “Under \(40\)” group, and \(15\) observations for the “\(40\) and over” group.
Provided the patients are not closely related, the patients are independent of each other. (If all \(15\) observations were all from the same family, for example, this would not be true.) The “patient” is the unit of analysis and the unit of observation.
Later, the researchers decide to take measurements from the left and right arms of every patient. Thus, there are now \(30\) observations for the “Under \(40\)” group, and \(30\) observations for the “\(40\) and over” group. However, the left and right arm measurements for each person are likely to be very similar. The “patient” is the unit of analysis, and each patient provides two observations (one from each arm).
A study compared two physical activity (PA) programs. Each of \(44\) children in the study, chosen from schools across the region, was allocated to one of two PA programs (with parental agreement). The children’s fitness was measured for every student at the end of the six-month study.
The units of observation are the students: fitness measurements are taken from each student. The units of analysis are also the students: students using the different programs are being compared. In addition, the PA program was allocated to each student individually, and each student has their own family routines and activities, etc. and lives separate, distinct lives. Each unit of analysis (student) has one unit of observation.
People in groups at the beach will probably not be independent: people in groups tend to behave similarly. For example, a couple will often (but not always) both be wearing or not wearing hats; friends often behave in similar ways.
Hence, the researchers may decide to use data from individual people, and not groups (“person” is the unit of analysis and unit of observation). Alternatively, the researchers may decide to use people groups as the unit of analysis (some will be groups of one), and record data from just one person in any group (e.g., the person closest to the researchers when the group is noticed).
Research studies usually include terms that must be carefully and precisely defined, so that others know exactly what words and terms mean, without ambiguity. Two types of definitions can be given when necessary.
In many cases, a clear operational definition is needed to describe how data will be collected to ensure repeatability and consistent data collection, by removing any ambiguity about how data are obtained.
An operational definition would describe how “stress” is measured, since stress cannot be measured directly (like height, for example). “Stress” could be measured using a questionnaire or measuring physical characteristics, for instance. Other ways of measuring stress are also possible, and all have advantages and disadvantages.
Sometimes the definitions themselves are not important; a clear definition is simply needed. To avoid confusion, commonly-accepted definitions should be used unless good reasons exist for using a different definition. When a commonly-accepted definition does not exist, the definition being used should be very clearly articulated, and the reason given if necessary.
Example2.64.Operational and conceptual definitions.
A research article [45] entitled “Shoulder range of motion and strength in young competitive tennis players with and without history of shoulder problems” provided these necessary conceptual definitions (among others):
Players, administrators and fans are wary of concussions and head injuries in sport. A conference on concussion in sport developed this conceptual definition[3]:
However, an operational definition is needed to explain how to identify a player with concussion during a game. Rugby decided on this operational definition[4]:
1. The presence, pitch side, of any Criteria Set 1 signs or symptoms (table 1)... [this table includes symptoms such as “convulsion”, “clearly dazed”, etc.];
An operational definition would explain how the temperature is measured: the thermometer type, how the thermometer was positioned, how long was it left in the water; and so on.
Eating occasions that occurred during breakfast, midday and evening meals were meals and all eating occasions that occurred between these meals were classified as snacking.
These are all conceptual definitions, explaining what the terms mean. An operational definition would explain how the data were obtained from the participants (e.g., using a food diary).
A study examined the possible relationship between the “pace of life” and the incidence of heart disease [33] in \(36\) US cities. The researchers used four different operational definitions for “pace of life” (remember the article was published in 1990!):
Suppose you notice some people taking echinacea (a herb) after they get a common cold. You may wonder: does taking echinacea help in any way with a cold? You may ask:
This RQ is clearly poor, but is a starting point. This RQ can be refined by clarifying the POCI elements. For example, what population is of interest? Many options exist: all residents of your country, or just adults in a specific part of your country. Some of these may not be practical (i.e., when a sample cannot easily be obtained that represents the population).
What outcome could be used to determine echinacea’s effectiveness? Options include the average cold duration, or the percentage of people who take days off work due to the cold.
The initial RQ is also vague: better than what? The outcome could be compared between groups (between those taking echinacea and the controls (those who do not)). A within-individuals comparison seems unsuitable for this RQ.
The study could also have intervention or not, which has implications for how the study is conducted and how the results are interpreted. If the study did not have an intervention, the subjects would decide for themselves how to treat their cold. If the study did have an intervention, the use of echinacea would be imposed by the researchers.
Many terms need defining, too. What is meant by “echinacea” (fresh? tablet form? as a tea?); “cold” (self-diagnosed? diagnosed by a doctor?), and so on.
Among Australian teenagers with a common cold, is the average duration of cold symptoms shorter for teens given a daily dose of echinacea, compared to teens taking no echinacea?
Statistical software packages are used to store data for subsequent analyses. Datasets that do not contain any within-individuals variables are organised so that:
In statistical software, the variable names are not placed in a row (say, in Row 1, above the data itself), which might happen when using a spreadsheet. The names of the variables are the names of the columns.
For this RQ, the two between-individuals variables are “Duration of cold symptoms” (response variable), and “Type of treatment” (explanatory variable). The person is the unit of analysis, so the number of rows in the data worksheet is the sample size. The data worksheet needs at least two columns (Figure 2.72):
An additional column may record the name or ID of each individual, and more columns may record other within-individuals variables (such as age and height of the individuals).
Screenshot of statistical software showing a dataset with rows for individuals and columns for variables, including duration of cold symptoms and type of treatment.
Figure2.72.Software prepared for data with no within-individuals variable. Each row represents an individual; each column represents a between-individuals variable.
Datasets that do contain within-individuals variables can be organised in wide or long format. Some analyses are easier using wide format, and some using long format.
In wide format, each row represents one individual (Figure 2.74, left panel). In long format, each individual is represented by multiple rows (Figure 2.74, right panel).
Figure2.74.Software prepared for data with a within-individuals variable; the same data is shown in both panels. Left: in wide format, with one individual per row. Right: in long format, with multiple rows per individual. Both include a column of identifying information.
In this chapter, you have learnt to write research questions for quantitative analysis. All research questions (RQs) study a population (P). Descriptive RQs study some outcome (O) in the population. Relational RQs compare the outcome between different groups of individuals (a between-individuals comparison). Repeated-measures RQs compare the same outcome when measured on the same individuals multiple times (a within-individuals comparison). Some RQs also have an intervention (I): when the values of the comparison can be manipulated by the researchers. Correlational RQs ask about the relationship between variables. RQs may be decision-making RQs (one- or two-tailed) or estimation RQs.
Data comes from a sample of individuals in the population. The outcome is a numerical summary of the values of the response variable from many individuals. Similarly, the data concerning the comparison comes from measuring or observing the values of the explanatory variables from individuals.
The who or what that observations are made from are called the units of observation. The smallest independent collections of units of observations (that is, independent examples of the population) are called the units of analysis.
For the following studies, determine whether the study is likely to use a between-individuals comparison or a within-individuals comparison. In each case, identify the outcome.
For the following studies, determine whether the study is likely to use a between-individuals comparison or a within-individuals comparison. In each case, identify the outcome.
Among Danish university students, is the average resting diastolic blood pressure the same for students who regularly drive to university and those who regularly ride bicycles to university?
a \(4\)-year (1995--1998) field study in a Peruvian peri-urban community... to examine the relation between diarrhea and nutritional status in \(230\) children \(\lt 3\) years of age
For Japanese adults with a common cold, do people who take vitamin C tablets daily have, on average, a shorter cold duration than people who do not take any vitamin C tablets?
Animals in an experiment are divided into pens (three animals per pen), and feed is allocated to each pen [77]. Animals in different pens receive different feed; animals in the same pen receive the same feed. The weight gain of each animal is recorded.
A research study was comparing the average length of Blue Gum eucalypt leaves in two areas of Queensland. A student takes \(40\) leaves from each of ten trees in Area A, and \(40\) leaves from each of ten trees in Area B.
[48] examined the strength needed to pull out nose-hairs. Fifty nose-hairs were pulled from one author’s nose, and \(50\) nose hairs pulled from the other author’s nose, and the average pull-out strengths for each man compared.
[52] placed different people into one of three different virtual-reality (VR) environments: trees, grass or concrete. Stress levels were measured using “skin conductance level” (SCL) for each individual, before and after exposure to the VR environment.
SCLs are an unbiased measure of sympathetic activity via the electric impulses on the skin’s surface and sweat glands, which are innervated only by the sympathetic nervous system...
For American adults, is the average number of recorded steps per day the same when recorded using both a waist accelerometer, and a wrist accelerometer?
For each RQ, classify these RQs as descriptive, relational, repeated-measures, or correlational RQs. Then, classify them as estimation or decision-making RQs. Does the study have an intervention?
[2] studied the relationship between daily sodium excretion and whether people had been diagnosed with diabetes or not, in Israeli adults. The study also explored the strength of the relationship between the daily sodium excretion and the systolic blood pressure.
Classify the two RQs as descriptive, relational, repeated-measures, or correlational RQs. Then, classify them as estimation or decision-making RQs. Does the study have an intervention?
[44] studied the incidence of musculoskeletal disorders in Iranian bus drivers. They introduced a program that aimed to provide relief for the drivers. Each bus driver was evaluated both before and after the intervention.
Classify the RQ as descriptive, relational, repeated-measures, or correlational RQs. Then, classify the RQ as estimation or decision-making RQs. Does the study have an intervention?
To determine the average length of the legs of emus, \(27\) emus from various zoos were studied. For each emu, the length of the left and right leg were recorded, resulting in \(54\) measurements.
A study compared the percentage of females and males that wear closed-in shoes to the supermarket. For each person they observed, the type of shoe on each person’s left and right foot (as either closed-in; not closed-in) was recorded. This approach resulted in \(310\) observations.
A study compares the wear on two brands of car tyres. Four tyres of Brand A are allocated to each of Cars 1--5, and four tyres of Brand B are allocated to each of Cars 6--10. After \(12\) months, the amount of wear is recorded on each tyre, and the two brands compared.
[67] discuss a scenario where six subjects with colorectal cancer underwent therapy. Another six similar subjects did not receive the therapy. The size of all the subjects’ removed lymph nodes were then measured. Each subject’s specimen (p. 6):
was divided into two sub-samples after collection [...] processed and analysed at two occasions, by different members of the laboratory team [...] Three slices per sub-sample were collected for each subject.
Bamboo is a fast-growing, strong grass often used for green building practices. A small research study explored the hardness of bamboo when used as flooring material.
The force required to embed an \(11.28\mms\) steel ball into wood to half the diameter of the ball.
of bamboo flooring provided by Bamboo Flooring Australia Pty Ltd was measured by the Queensland Department of Primary Industries [17]. Five floorboards were taken, and two hardness measurements were taken on each board (units not given, but probably kilonewtons; Table 2.75).
Suppose the measurements were taken from \(10\)different places on the same board (rather than from five different boards). How many units of analysis are there now? Explain your answer.
