Hypothesis - How do the Null hypothesis and alternative hypothesis fit into the overall explanation of hypothesises?

[MathHelp]

Hi team,

It is common for a hypothesis to be described as an "explanation" for something or an event. But in statistics we use:

Null hypothesis: Population characteristic = observed characteristic.

Alternate hypothesis 1:  Population characteristic [greater than] observed characteristic.

Alternate hypothesis 2:  Population characteristic [less than] observed characteristic.

Alternate hypothesis 3:  Population characteristic [not equal to] observed characteristic.

A statistic study is conducted in order to obtain evidence/proof for an alternate hypothesis. If enough evidence/proof is found is support of an alternate hypothesis then the null hypothesis can be rejected in favour of it.

But these hypothesises don't seem to offer explanations. They can also hardly be judged using the criteria of adequacy, internal consistency, external consistency, and fruitfulness.

 

Any input is welcome...

[studiot]

9 minutes ago, MathHelp said:

But these hypothesises don't seem to offer explanations. They can also hardly be judged using the criteria of adequacy, internal consistency, external consistency, and fruitfulness.

Indeed not.

But then adequacy, internal consistency, external consistency, and fruitfulness are not scientific terms in general nor  statistical terms in particular.

Think about it.

You have already stated the difference between a statistical hypothesis and a logical conclusion drawn from premises., notably you have several hypothesis any of which could account for the data.

That is the null hypothesis only ever concludes that the hypothesis could account for the data, and usually that it is the most likely of several hypotheses

It never actually concludes that the hypothesis does account for the data.

By contrast a sound or valid logical conclusion formally excludes other hypotheses, given the validity of the premises.

 

[MathHelp]

Apologies, I didn't understand your response. 

Hypothetical reasoning is a form of induction (not deduction). A hypothesis is used to explain an event or to help conceptualize something.

Induction: premises suggest the conclusion is true (but it could be wrong).

Deduction: the premises imply the certainty of the conclusion (assuming the premises are true).

I understand that later on in the scientific process that deduction would be used when looking for implications of the hypothesis - but that is not related to what a hypothesis is/is not. 

What I am wanting to know is how do philosophers/logicians incorporate null/alternate hypothesises into there ideas about what a hypothesis is and how they work. 

Quote

But then adequacy, internal consistency, external consistency, and fruitfulness are not scientific terms in general nor  statistical terms in particular.

That's the key right there - I am not wanting to know where adequacy, consistency, fruitfulness etc etc fit within chemistry (the coolest science)or statistics. I want to know where null hypothesis and alternate hypothesis fit within philosophy.

It's a philosophy question.

Thanks for your response though.

[Genady]

An alternative hypothesis explains something as cause and effect, while a null hypothesis explains it as a statistical fluke.

[studiot]

I am saying that whilst the term hypothesis is a general scientific and philosophical term meaning a proposal that may be (is hoped to be) valid,

the term 'null hypothesis' is a specifically statistical term that means something more and has to be set in a way that can be numerically compared.

There is for instance a form of descriptive statistics that cannot have a null hypothesis.

5 minutes ago, Genady said:

An alternative hypothesis explains something as cause and effect, while a null hypothesis explains it as a statistical fluke.

How does that square with the opening post examples ?

Edited December 12, 2022 by studiot

[Genady]

Regarding the opening post examples:

Null hypothesis: a deviation from an observed characteristic is a fluke,

Alternative 1: a deviation is caused by population characteristic being greater than observed characteristic.,

etc. 

[studiot]

23 minutes ago, Genady said:

Regarding the opening post examples:

Null hypothesis: a deviation from an observed characteristic is a fluke,

Alternative 1: a deviation is caused by population characteristic being greater than observed characteristic.,

etc. 

That's not how I read it, though I will grant you that the opening post is not strictly correctly formulated, as the stated null hypothesis is not actually a null hypothesis at all.

Edited December 12, 2022 by studiot

[MathHelp]

Quote

That's not how I read it, though I will grant you that the opening post is not strictly correctly formulated, as the stated null hypothesis is not actually a null hypothesis at all.

Oh, but I learned that from a textbook. Can you tell me what is wrong with it and what the correct formulation would be?

[MathHelp]

21 hours ago, Genady said:

Regarding the opening post examples:

Null hypothesis: a deviation from an observed characteristic is a fluke,

Alternative 1: a deviation is caused by population characteristic being greater than observed characteristic.,

etc. 

Thanks, that makes perfect sense to me according to my understanding of null and alternate hypothesis. But I am still confused by studiot saying I have not formalised the null hypothesis correct - can you see any errors???

[studiot]

3 hours ago, MathHelp said:

Oh, but I learned that from a textbook. Can you tell me what is wrong with it and what the correct formulation would be?

I'm glad to see that you are reading posts carefully. +1

I can tell this is a statistics textbook or part of the book because 'population' is special statistics term, like 'null hypothesis.'

23 hours ago, MathHelp said:

Null hypothesis: Population characteristic = observed characteristic.

Now strictly the population refers to the entire set of objects possessing the characteristic or property being observed or measured.

It is usually not practicable or sometimes even possible to measure this characteristic for every object in the population, only for some of them.

So the observations form a perhaps incomplete dataset called the 'sample'.

So there are three variables in play; the population, the characteristic and the sample.

An example may make this clearer.

 

Consider a sack of potatoes, or perhaps a pile of aggregate (stones) for making concrete. 

The sack or the pile would be the population.

We might be interested in the average size of the pebbles or the potatoes. That would be the characteristic or property.

We could, of course, measure the size of every pebble or every potato but that would be impractical so we take a sample and only measure the sizes in that sample.

(Note sometimes we can and do use the entire population say marks for students in a class so in that case the sample is the same as the population)

Coming back to your null hypothesis, what we want is reassurance that our sample correctly represents the population so our null hypothesis should be

The average size in the entire population is the same as the average of the measure sizes in the sample.
We can (should) add to the the 'confidence level' or probability that this is a corrct statement.

An alternative null hypothesis is

The sample data could have come from the population as unbiased data.

This is version is important to check our sampling technique.
For example with the pile of stones the larger ones tend to roll down to the bottom at the sides so if we just take a shovel of these we will get an overestimate of the pebble size.

So back to your book's statement.

"Null hypothesis: Population characteristic = observed characteristic."

You can only use the NH in this form if you know the population characteristic as with the average class mark.

In which case it is no longer a hypotheses but an identity.

 

Does this help.

 

By the way forming a good null hypothesis can make all the difference to the quality of a statistical analysis.

 

[MathHelp]

Thanks for the explanation.

Quote

Now strictly the population refers to the entire set of objects possessing the characteristic or property being observed or measured.

It is usually not practicable or sometimes even possible to measure this characteristic for every object in the population, only for some of them.

So the observations form a perhaps incomplete dataset called the 'sample'.

So there are three variables in play; the population, the characteristic and the sample.

I think it might just be a variation in focus. There are many instances where we have all the data for a population so the null hypothesis can still be population versus sample.

For example, you may be doing an analysis of the population of workers in your company that do a task one way versus a sample of workers that have learned to do the task using a different process. In which case it is population versus sample. 

I learned statistics for Analytical Chemistry so the emphasis was on calibration of instruments. Effectively it was comparisons of known value (so what in other contexts would be "population" characteristic) versus observed value of the sample.

With that said, I appreciate you pointing this out to me because for most of the time I was learning statistics the textbook kept giving population versus sample null hypothesises but the in-class examples were all sample versus sample (the stats course was not specific to analytical chemistry) so I did find it confusing, and I would have loved for someone to identify this possible source of confusion.