Can anyone help me with a study/homework question?

[Whoneedsleep]

It should be simple but I can not find the answer anywhere and it’s driving me mad! I think I must have stared at it for hours now.

A researcher conducts a study. Is there any difference between the following statements and if so what is their actual meaning?

1. Tests showed that 7 out of 10 children prefer product A
2. Tests showed that 7 out of every 10 children preferred product A

If it changes anything there were 100 children in the study and 74 preferred product A.

Please can someone explain the difference between the two statements before my head explodes? Is there any significant different between it being 7-10 and 7 out of every 10? Surely they mean the same thing or is my grammar so bad I can’t understand the difference?

Thanks in advance!!

The first one refers only to the study.
The second one EXTRAPOLATES from the study and comes to a conclusion on the wider population.

@heldinadream thank you so much! Finally something to look up!!

I’ve looked at the question so long my mind has drawn a complete blank.

To be honest I think it's a bit more nuanced than that but I've got covid and I'm feeling like shit so I can't get my brain to do any better. Glad it's helpful - it's a start anyway!

Is the change from prefer to preferred deliberate?

I think you're focused on the wrong part. It's not so much the numbers but the "prefer" versus "preferred". The results only shows that 7/10 in the study preferred something. Whether you can say that means people outside the study prefer it is debatable. The sample size of the population can be used to determine if the sample is representative. If the population is homogeneous and the sample size representative then A is true, otherwise you can only comment on the preference of the people studied so only b is true.

Unless you make shampoo, then if one punter online says they like it better than the Aldi dupe you say that 100% of users say it's the best 😂

1. states a fact eg 7 children out of each ten in the study preferred the product - actually 7.4 children in each ten but you can’t have 0.4 of a child
2. implies that if you take this across the county, school, country etc you can assume 7 out of every 10 children will prefer it

however from the data point of view your study could have been done on primary school children or year 1, for example, so wrong to assume secondary might have the same data. Or the questions might have been slanted to get the answer you wanted. also taste differ and it doesn’t take into account allergies or those children that can’t have the product eg in hospital etc so the data has limitations that you need to be aware of before making mass assumptions

I would interpret it as follows

7 out of 10: out of the 100, they chose 10 and 7 of those preferred it.

7 out of every 10: no matter which 10 they chose 7 of them would always prefer it. With this wording you can conclude on average 70% of the whole group preferred it.

With 7 out of 10 you can't make conclusions that can be applied to the whole group.

Thank you all so much!

The question is worded exactly like that @marcopront

I hadn’t really thought about the difference between prefer or preferred, I’ve been so stuck on the 7/10 vs 7 out of every 10 part of the question.

The subject is about interpreting studies and statistics, rather than the content of the study itself if that changes anything.

Without seeing the exact wording it's hard to know. My answer is opposite to everyone else I notice... But based on what you said this is about whether you can extrapolate results of a study beyond the study cohort. Read up about sample sizes, population homogeneity and significance.

The questions asks:

Read the following statements and comment on their actual meaning, including whether or not either of these statements are statistically significant.

Other than that I have the basic facts of the study (ie 100 participants, 70 preferred product A) Theres no other information about the study itself as it’s hypothetical.

I hate things like this it’s really not a strength of mine, I tend to overthink massively and get stuck for ages when the answer is probably so simple!

My read on this:

The researcher conducts a study of 100 children.

The actual test showed 74 of the 100 children preferred Product A.

Both statements at first seem to be different but both correct.

However the second statement misses the word ‘children’ out.

The first statement could be read literally to mean only 10 children were tested, not 100.

The second statement, adjusted to include the word children would be most accurate in my view.

Does that help!?

Don't stress, lies damn lies and statistics eh! Don't get hung up on the wording around the numbers, that's a red herring.

I stand by my first answer.

You know that B is true because it's only refering to the people in the study. You can't know if A is true without knowing more about the population because its an extrapolation beyond the people in the study. You can't know about the statistical significance without the population size. You could say what size population the result would be valid for, given a certain confidence interval, or intervals.

Hopefully this all points you in the right direction to read up. There's lots on info online about basic stats. Good luck!

The second statement is the only statement to indicate 100 children were tested.

The first statement only indicates 10 were tested.

Are you meant to do an actual stats test to see if the results are statistically significant? A statement cannot be statistically significant. Results are significant to a certain probability value.

I'm also not sure the statements have an "actual meaning"- as different people are inferring different things from them.

I don't think this is you, I think it's a badly worded question.

Is what they're going for that the initial statement implies only 10 children were surveyed or something?

Without the context of knowing that 100 children were tested, I would understand this as:

1: Tests showed that 7 out of 10 children prefer product A (There were 10 children and 7 of them preferred product A)
2: Tests showed that 7 out of every 10 children preferred product A (There were multiple sets of 10 children, and in each set 7 preferred product A)

But I'd go on to suggest that [1] is sufficiently loosely/colloquially worded that you could still extrapolate it to mean that 70% of (an indeterminate set of) children preferred product A. Hence, lessons to learn [a] ensure context and supporting info is explicit and referenced, and [b] check that wording cannot be subject to misunderstanding.

I assumed that the prefer/preferred thing was to do with the presentation of the evidence. If you say "preferred" then there is an implication that you are referring to the specific results of this study; "prefer" implies a continuous state, and thus you could pick any 10 children and the results would be the same.