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GCSE · Statistics

S11 Experimental Design

EDEXCEL 1ST0 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A researcher wants to find out whether adding fertiliser increases the height that tomato plants grow to.

(a)State what is meant by a hypothesis.(1)

(b)Write a suitable hypothesis for this investigation.(1)

(Total for Question 1 is 2 marks)

For each statement about experimental investigations, write down whether it is True or False.

(i)A hypothesis must be written as a question, rather than as a statement.(1)

(ii)A control group experiences the same conditions as the treatment group, except for the variable being tested.(1)

(iii)The independent (explanatory) variable is the one that is measured as the outcome of the experiment.(1)

(Total for Question 2 is 3 marks)

A scientist plans two separate experimental investigations, described in the table below.

Investigation	Description
1	Testing whether the amount of daily sunlight affects the height a sunflower grows to
2	Testing whether the temperature of water affects the time taken for an ice cube to melt

(a)For Investigation 1, identify the explanatory (independent) variable and the response (dependent) variable.(2)

(b)For Investigation 2, identify the explanatory (independent) variable and the response (dependent) variable.(2)

(Total for Question 3 is 4 marks)

A pharmaceutical company is testing whether a new painkiller reduces headache pain. 200 volunteers with headaches are split into two groups, as shown below.

(a)State which group, A or B, is the control group.(1)

(b)Explain the purpose of including a control group in this investigation.(2)

(Total for Question 4 is 3 marks)

For the painkiller trial in Question 4 to be a fair test, several variables must be kept the same for both groups.

(a)Give two variables, other than which tablet is given, that should be kept the same (constant) between Group A and Group B.(2)

(b)Explain why it is important to keep these variables constant between the two groups.(2)

(Total for Question 5 is 4 marks)

In the painkiller trial, some volunteers in Group A happen to have less severe headaches to start with than volunteers in Group B, purely by chance. This is an example of an extraneous variable.

(a)State what is meant by an extraneous variable.(1)

(b)Explain how this extraneous variable (different initial headache severity) could affect the conclusions of the trial.(2)

(Total for Question 6 is 3 marks)

To reduce the effect of extraneous variables like the one in Question 6, the 200 volunteers should be randomly allocated to Group A or Group B.

(a)Describe one method the company could use to randomly allocate volunteers to the two groups.(1)

(b)Explain why randomly allocating volunteers to groups is better than allowing volunteers to choose their own group.(2)

(c)State one variable, other than which tablet is received, that random allocation would help to balance between the two groups.(1)

(Total for Question 7 is 4 marks)

A student is investigating how the length of a pendulum affects the time for one swing. For a pendulum of length 40 cm, she repeats her timing 3 times, shown in the table.

Repeat	1	2	3
Time (seconds)	1.28	1.42	1.25

(a)Work out the mean time for one swing at this length, giving your answer to 3 significant figures.(2)

(b)Give one reason why taking repeated timings and calculating a mean gives a more reliable result than using a single timing.(1)

(c)State one further change the student could make to her investigation to improve its reliability even more.(1)

(Total for Question 8 is 4 marks)

In the painkiller trial, volunteers are not told whether they have been given the new painkiller or the placebo. This is called a blind trial.

(a)State what is meant by a double-blind trial.(1)

(b)Explain why it is useful for volunteers not to know which tablet they have received.(2)

(c)Explain why it is also useful for the researcher recording results not to know which volunteer received which tablet.(1)

(Total for Question 9 is 4 marks)

A garden centre wants to test whether a new plant feed increases the average height that tomato plants grow to after 8 weeks. They have 60 tomato plants of the same variety and age available.

(a)Write a suitable hypothesis for this investigation.(1)

(b)Identify the explanatory (independent) variable and the response (dependent) variable for this investigation.(2)

(c)State which group of plants should act as the control group.(1)

(d)Give two variables, other than the feed, that should be kept constant between the two groups of plants, and explain why this matters.(2)

(Total for Question 10 is 6 marks)

A market researcher wants to collect people's opinions on a new bus route, either using face-to-face interviews or a written questionnaire.

(a)Give one advantage of using face-to-face interviews rather than a written questionnaire for collecting this data.(1)

(b)Give one advantage of using a written questionnaire rather than a face-to-face interview for collecting this data.(1)

(c)Give one way in which the interviewer could affect the quality of the data collected in a face-to-face interview, that would not happen with a written questionnaire.(1)

(Total for Question 11 is 3 marks)

A student's investigation into whether energy drinks affect reaction time follows the statistical enquiry cycle shown below.

(a)As well as writing a hypothesis and deciding the control group, constants and random allocation, state one other decision that should be made about the design at the plan stage.(1)

(b)State the stage of the cycle at which the student would calculate a mean of repeated reaction time measurements, to help remove the effect of random error.(1)

(c)At the interpret stage, the student concludes that energy drinks improve reaction time. Explain why a control group was essential for her to reach this conclusion.(2)

(Total for Question 12 is 4 marks)

A student investigates whether listening to music improves memory. She asks for volunteers, then lets them choose whether to join the 'music' group or the 'no music' group. All volunteers in the music group complete the memory test in the morning; all volunteers in the no-music group complete it in the afternoon. Each volunteer attempts the test only once.

(a)Identify one weakness in how the volunteers are placed into groups, and explain the problem this could cause.(2)

(b)Identify one weakness in how the test is timed, and explain the problem this could cause.(2)

(c)Suggest one change, relating to the number of times each volunteer attempts the test, that would make the experiment more reliable.(1)

(Total for Question 13 is 5 marks)

Two students each investigate the same hypothesis: that a stretched elastic band travels further when pulled back further. Student A tests 1 elastic band, with 3 repeats at each pull-back distance. Student B tests 10 different elastic bands, with 3 repeats at each pull-back distance for each band.

(a)Explain why Student B's investigation is likely to give more reliable conclusions about elastic bands in general than Student A's.(2)

(b)Both students take 3 repeat readings at each distance rather than 1. State what they should do with the 3 repeat readings before using them to draw a conclusion.(1)

(c)At one pull-back distance, Student A records these three repeat distances travelled: 42 cm, 45 cm, 41 cm. Work out the range of these three readings.(1)

(Total for Question 14 is 4 marks)

In an investigation into whether a new teaching app improves test scores, students who use the app also happen to spend more time revising overall than students who do not use the app.

(a)Explain why 'time spent revising' is a confounding variable in this investigation.(2)

(b)State one change to the experimental design that would prevent this variable from confounding the results.(1)

(Total for Question 15 is 3 marks)

A researcher wants to test whether a new toothpaste tastes better than a leading competitor's toothpaste, using a blind taste test with 40 volunteers.

(a)Explain how the researcher could make this a blind trial for the volunteers.(1)

(b)Explain why it would be very difficult to make this trial double-blind.(2)

(c)Suggest one practical way the researcher could reduce this problem, without needing the person running the test to know the brands.(1)

(Total for Question 16 is 4 marks)

A pharmaceutical trial for a new painkiller measures the percentage of volunteers reporting reduced pain after treatment, for trials of different sizes.

Trial size (volunteers)	20	200	2000
% reporting reduced pain	75%	61%	60%

(a)State which trial size is likely to give the most reliable estimate of the true percentage of people helped by the painkiller, giving a reason.(2)

(b)Give a reason why the trial with only 20 volunteers might give a result that does not reflect how the drug performs in the wider population.(1)

(Total for Question 17 is 3 marks)

A company claims its new energy bar improves marathon runners' finishing times. To test this, they ask 12 runners from the same running club to eat the energy bar before their next race, then compare their times to their personal best times from previous races (without the energy bar). All 12 runners know they are testing the new energy bar.

Evaluate the design of this investigation, referring to at least three different weaknesses and the effect each has on the validity of the conclusions.

(Total for Question 18 is 5 marks)

Mark scheme · S11 Experimental Design

Question 1

(a) B1 a statement that can be tested/investigated and predicts a relationship between two variables, oe
(a) Answer: A hypothesis is a statement that can be tested by an investigation, which predicts a relationship between two variables.
(b) B1 a testable statement linking fertiliser and plant height, e.g. 'plants given fertiliser grow taller than plants not given fertiliser', oe
(b) Answer: Tomato plants given fertiliser will grow taller than tomato plants not given fertiliser.

Question 2

(i) B1 False cao
(i) Answer: False
(ii) B1 True cao
(ii) Answer: True
(iii) B1 False cao
(iii) Answer: False

Question 3

(a) B1 explanatory (independent) variable: amount of daily sunlight cao
(a) B1 response (dependent) variable: height the sunflower grows to cao
(a) Answer: Explanatory: amount of daily sunlight. Response: height the sunflower grows to.
(b) B1 explanatory (independent) variable: temperature of the water cao
(b) B1 response (dependent) variable: time taken for the ice cube to melt cao
(b) Answer: Explanatory: temperature of the water. Response: time taken for the ice cube to melt.

Question 4

(a) B1 B cao
(a) Answer: Group B
(b) B1 allows the effect of the new painkiller to be compared with what happens without it (with only a placebo), oe
(b) B1 so that any change in pain can be attributed to the drug itself, rather than to another cause such as the placebo effect, oe
(b) Answer: A control group gives a comparison: it shows what would happen without the new drug, so any extra improvement in Group A can be attributed to the drug itself, rather than to another cause such as volunteers simply believing they had been treated.

Question 5

(a) B1 any valid constant, e.g. the dosage/size of tablet given
(a) B1 a different valid constant, e.g. how and when pain is measured/recorded, or the length of the trial
(a) Answer: e.g. the dose (size) of the tablet, and how/when pain levels are recorded.
(b) B1 identifies that if these variables were different between groups, any difference in outcome might be caused by them rather than by the tablet
(b) B1 so keeping them the same makes the comparison fair, meaning any difference in pain reduction can be attributed to the tablet, oe
(b) Answer: If these variables were not kept the same, any difference in pain reduction between the groups could be caused by them rather than by the tablet. Keeping them constant makes the comparison fair, so the tablet is the only likely explanation for any difference.

Question 6

(a) B1 a variable, other than the one being investigated, that could affect the results if it is not controlled, oe
(a) Answer: An extraneous variable is any variable, other than the one being tested, that could affect the results of the investigation if it is not controlled.
(b) B1 if Group B started with more severe headaches, it may appear to improve less, even if the drug is equally effective
(b) B1 so any difference between the groups might be due to this extraneous variable rather than (only) the drug, making the conclusion unreliable
(b) Answer: If Group B started with worse headaches, they might appear to improve less than Group A even if the drug works equally well for both. The difference seen could then be caused by the difference in starting severity, rather than by the drug alone, making the conclusion unreliable.

Question 7

(a) B1 any valid random method, e.g. number each volunteer and use a random number generator/table to assign each one to a group, oe
(a) Answer: Give each volunteer a number, then use a random number generator to decide which group each numbered volunteer joins.
(b) B1 random allocation spreads extraneous variables (e.g. headache severity, age) roughly evenly between the two groups
(b) B1 this reduces bias, so any difference in outcome is more likely due to the drug rather than a systematic difference between the groups, oe
(b) Answer: Random allocation spreads other variables, such as age or headache severity, roughly evenly between the two groups, reducing bias. If volunteers chose their own group, one group might end up systematically different (e.g. more severe cases choosing the new drug), making the comparison unfair.
(c) B1 any valid extraneous variable, e.g. age, gender, initial headache severity
(c) Answer: e.g. the volunteers' ages.

Question 8

(a) M1 (1.28 + 1.42 + 1.25) / 3, oe
(a) A1 1.32 (seconds) cao, awrt
(a) Answer: 1.32 seconds
(b) B1 reduces the effect of random error/an unusual anomalous timing in any one individual reading, oe
(b) Answer: It reduces the effect of random error, so an unusually fast or slow individual timing has less effect on the overall result.
(c) B1 any valid improvement, e.g. increase the number of repeats, or test more pendulum lengths, oe
(c) Answer: e.g. take more repeat timings at each length.

Question 9

(a) B1 a trial in which neither the volunteer/participant nor the researcher recording the results knows which group (treatment or placebo) each volunteer is in, oe
(a) Answer: A double-blind trial is one in which neither the volunteer nor the researcher recording results knows which group (treatment or placebo) each volunteer is in.
(b) B1 if volunteers knew, those given the real drug might expect to feel better and report more improvement (or vice versa)
(b) B1 blinding removes this bias (the placebo effect), so the comparison between groups is fairer/more valid, oe
(b) Answer: If volunteers knew which tablet they had, those given the real drug might expect it to work and report feeling better regardless (the placebo effect). Keeping them blind removes this bias, so the comparison between the groups is fairer.
(c) B1 prevents the researcher from (consciously or unconsciously) treating, recording or interpreting the two groups differently, oe
(c) Answer: It stops the researcher from treating, recording or interpreting results differently for the two groups, even unintentionally.

Question 10

(a) B1 a testable statement linking plant feed and height, e.g. 'plants given the new feed grow taller than plants not given it', oe
(a) Answer: Tomato plants given the new plant feed grow taller after 8 weeks than tomato plants not given the feed.
(b) B1 explanatory (independent) variable: whether the plant is given the new feed cao
(b) B1 response (dependent) variable: height of the plant after 8 weeks cao
(b) Answer: Explanatory: whether the plant is given the new feed. Response: the plant's height after 8 weeks.
(c) B1 the group of plants not given the new feed (grown under otherwise identical conditions), oe
(c) Answer: The group of plants that is not given the new feed, but is grown under otherwise identical conditions.
(d) B1 gives two valid constants, e.g. amount of water/sunlight given, pot size, soil type
(d) B1 explains that keeping them the same means any difference in height can be attributed to the feed rather than to another factor, oe
(d) Answer: e.g. the amount of water and sunlight each plant receives should be kept the same. This matters because, if they were different, any difference in height could be caused by these factors rather than by the plant feed.

Question 11

(a) B1 any valid advantage, e.g. the interviewer can clarify a question the person does not understand, giving more accurate/complete answers, oe
(a) Answer: The interviewer can explain a question if someone does not understand it, leading to clearer, more complete answers.
(b) B1 any valid advantage, e.g. respondents may answer more honestly with no interviewer present, or it is cheaper/quicker to reach many people, oe
(b) Answer: Respondents may give more honest answers without an interviewer present, and it is quicker and cheaper to send to many people.
(c) B1 interviewer bias, e.g. the interviewer's tone, wording or body language could influence how a person answers, oe
(c) Answer: The interviewer's tone or body language could influence how someone answers (interviewer bias), which cannot happen with a written questionnaire.

Question 12

(a) B1 any valid design decision, e.g. sample size/number of repeats, or how the response variable will be measured, oe
(a) Answer: e.g. how large a sample to use, or how many repeats to take.
(b) B1 process cao
(b) Answer: Process
(c) B1 without a control group there would be nothing to compare the energy drink group's reaction times against
(c) B1 so only by comparing the processed data from both groups at the interpret stage can any change in reaction time be attributed to the energy drink itself, oe
(c) Answer: Without a control group, there would be no comparison to show what reaction times would be without an energy drink. Comparing the processed results from both groups is the only way to attribute any improvement to the drink itself, rather than to another cause.

Question 13

(a) B1 volunteers are not randomly allocated to groups (they self-select)
(a) B1 this could introduce bias, e.g. people who already enjoy/respond well to music opting into the music group, an extraneous variable other than music that could affect memory
(a) Answer: The volunteers were not randomly allocated; they chose their own group. This could introduce bias, since the kind of person who chooses the music group (e.g. someone who already concentrates well with music) might have performed better on the memory test anyway.
(b) B1 time of day is not kept constant between groups (morning vs afternoon), an extraneous variable
(b) B1 memory performance may naturally differ by time of day, so time of day (rather than music) could explain any difference between the groups, oe
(b) Answer: Time of day is not kept the same: one group is tested in the morning, the other in the afternoon. Memory performance can naturally vary through the day, so any difference between the groups could be caused by the time of day rather than by the music.
(c) B1 repeat the test / give each volunteer several attempts and use a mean, oe
(c) Answer: Give each volunteer several attempts at the test and use their mean score, rather than a single attempt.

Question 14

(a) B1 testing more elastic bands means the results are less affected by one unusual/faulty band
(a) B1 so the conclusion is more likely to generalise to elastic bands in general, rather than just to the one band Student A tested, oe
(a) Answer: Testing 10 different bands means the result is not dominated by one unusually stretchy or weak band. This means Student B's conclusion is more likely to apply to elastic bands in general, whereas Student A's only tells her about the one band she used.
(b) B1 calculate the mean of the 3 repeats, oe
(b) Answer: Calculate the mean of the 3 repeat readings.
(c) B1 4 (cm) cao
(c) Answer: 4 cm

Question 15

(a) B1 it is linked to using the app (app users happen to revise more)
(a) B1 and it could itself affect test scores, so it is impossible to tell whether any improvement is due to the app or to the extra revision time, oe
(a) Answer: Time spent revising is linked to using the app (app users revise more overall), and extra revision could itself improve test scores. This makes it impossible to tell whether any improvement is due to the app or simply to the extra time spent revising.
(b) B1 e.g. randomly allocate students to app/no-app groups and keep total revision time the same/monitored for both groups, oe
(b) Answer: Randomly allocate students to the app and no-app groups, and make sure total revision time is kept about the same for both groups.

Question 16

(a) B1 use plain, unlabelled/coded containers so volunteers cannot see which toothpaste is which brand, oe
(a) Answer: Put each toothpaste sample in a plain, unlabelled container marked only with a code, so volunteers cannot see which brand they are tasting.
(b) B1 whoever sets up/hands out the samples usually needs to know which brand is which, in order to give out the right sample and record which was tasted
(b) B1 so that person (even unintentionally) could influence volunteers' responses, or record/interpret results differently for each brand, oe
(b) Answer: The person running the test usually needs to know which coded sample is which brand, in order to hand out the correct sample and record results accurately. This means that person could, even unintentionally, influence a volunteer's response or interpret results differently depending on the brand.
(c) B1 a third party, not involved in running the test, codes the samples, and the code is only revealed after all results have been recorded, oe
(c) Answer: Have someone not involved in running the test label the samples with a code, and only reveal which code matches which brand after all the results have been recorded.

Question 17

(a) B1 2000 cao
(a) B1 larger sample sizes are less affected by chance/random variation, so the result is more likely to be close to the true population percentage, oe
(a) Answer: The trial of 2000 volunteers. Larger samples are less affected by chance variation, so its result is more likely to be close to the true percentage for the whole population.
(b) B1 small samples are more affected by random/chance variation, so an unusual result is more likely to occur by chance, oe
(b) Answer: With only 20 volunteers, chance variation has a much bigger effect, so an unusually high or low result is more likely to occur just by chance.

Question 18

B1 no control group: all 12 runners receive the energy bar, so there is nothing to compare against to isolate its effect, oe
B1 no blinding: knowing they have the 'new' bar could create a placebo effect (expecting to run faster), biasing times regardless of the bar's real effect
B1 comparing to personal bests does not hold other variables constant, e.g. weather, course or the runner's current fitness could differ from the earlier race and confound the comparison, oe
B1 the sample is small (12) and drawn entirely from one running club, so it may not be representative of marathon runners generally, limiting how far conclusions can be generalised
B1 an overall judgement is given, e.g. the conclusion that the bar improves times is not well supported without a randomised, controlled, blind design comparing to a genuine control group under matched race conditions
Answer: The design is weak. There is no control group, so there is nothing to isolate the bar's effect from other causes. Runners are not blinded, so knowing they have the new bar could create a placebo effect. Comparing to personal bests does not control for other variables such as weather, course or current fitness. The sample is also small and drawn from a single club, limiting how far results can be generalised. Overall, the claim is not well supported without a randomised, controlled, blind trial comparing matched groups under the same conditions.

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