Tölfræði

Learning statistics with Jamovi

**Belief bias effect**

If you ask people to decide whether a particular argument is logically

valid, we tend to be influenced by the believability of the conclusion, even when we shouldn’t.

**Simpson’s paradox**

 Statistical phenomenon where an association between two variables in a population emerges, disappears or reverses when the population is divided into subpopulations. Ex. Berkeley gender bias.

**Measurement**

My **age** is *33 years,* the **bolded part** is “the thing to be measured”, and the *italicized* part is “the measurement itself”.

**Operationalisation**

The process by which we take a meaningful but somewhat vague concept and turn it into a precise measurement

**A theoretical construct**

This is the thing that you’re trying to take a measurement of,

like “age”, “gender” or an “opinion”. A theoretical construct can’t be directly observed, and often they’re actually a bit vague.

**A variable**

What we end up with when we apply our measure to something in the world. That is, variables are the actual “data” that we end up with in our data sets.

**Nominal scale**

There is no particular relationship between the different possibilities. For these kinds of variables it doesn’t make any sense to say that one of them is “bigger’ or “better” than any other one, and it absolutely doesn’t make any sense to average them. The classic example for this is “eye color”. Eyes can be blue, green or brown, amongst other possibilities, but none of them is any “bigger” than any other one. 

**Ordinal scale**

There is a natural, meaningful way to order the different possibilities, but you can’t do anything else. You can say that the person who finished the race first was faster than the person who finished second, but you don’t know how much faster.

**Interval scale**

The numerical value is genuinely meaningful. In the case of interval scale

variables the differences between the numbers are interpretable, but the variable doesn’t have a “natural” zero value. A good example of an interval scale variable is measuring temperature in degrees celsius.

**Ratio scale**

Zero really means zero, and it’s okay to multiply and divide. A good psychological example of a ratio scale variable is response time.  Suppose that Alan takes 2.3 seconds to respond to a question, whereas Ben takes 3.1 seconds. As with an interval scale variable, addition and subtraction are both meaningful here. Ben really did take 3.1-2.3 = 0.8 seconds longer than Alan did. However, notice that multiplication and division also make sense here too: Ben took 3.1Þ/2.3 = 1.35 times as long as Alan did to answer the question.

**A continuous variable**

 Is one in which, for any two values that you can think of, it’s always logically possible to have another value in between. 

If Alan takes 3.1 seconds and Ben takes 2.3 seconds to respond to a question, then Cameron’s response time will lie in between if he took 3.0 seconds. And of course it would also be possible for David to take 3.031 seconds to respond, meaning that his RT would lie in between Cameron’s and Alan’s.

**A discrete variable**

Is, in effect, a variable that isn’t continuous. For a discrete variable it’s sometimes the case that there’s nothing in the middle.

Although “2nd place” does fall between “1st place” and “3rd place”, there’s nothing that can logically fall in between “1st place” and “2nd place”

**Likert scale:**

(1) Strongly disagree

(2) Disagree

(3) Neither agree nor disagree

(4) Agree

(5) Strongly agree

\
It’s not interval scale, but in practice it’s close enough that we usually think of it as being quasi-interval scale.

**Reliability**

Tells you how precisely you are measuring something. It refers to the repeatability or consistency of your measurement. The measurement of my weight by means of a “bathroom scale” is very reliable. If I step on and off the scales over and over again, it’ll keep giving me the same answer.

**Test-retest reliability**

This relates to consistency over time. If we repeat the measurement at a later date do we get the same answer? 

**Inter-rater reliability**

This relates to consistency across people. If someone else repeats the measurement (e.g., someone else rates my intelligence) will they produce the same answer? 

**Parallel forms reliability**

This relates to consistency across theoretically-equivalent measurements. If I use a different set of bathroom scales to measure my weight does it give the same answer? 

**Internal consistency reliability**

 If a measurement is constructed from lots of different parts that perform similar functions (e.g., a personality questionnaire result is added up across several questions) do the individual parts tend to give similar answers?

**Independent variable**

The variable that you use to do the explaining

**Dependent variable** 

The variable that is being explained

Validity

Having a sound basis in logic or fact. Can you trust the result of your study?

Internal validity

Refers to the extent to which you are able draw the correct conclusions about the causal relationships between variables.

External validity

Relates to the generalisability or applicability of your findings. That is, to what extent do you expect to see the same pattern of results in “real life” as you saw in your study.

Construct validity

Question of whether you’re measuring what you want to be measuring. A measurement has good construct validity if it is actually measuring the correct theoretical construct, and bad construct validity if it doesn’t.

Face validity

Refers to whether or not a measure “looks like” it’s doing what it’s supposed to, nothing more. If I design a test of intelligence, and people look at it and they say “no, that test doesn’t measure intelligence”, then the measure lacks face validity.

Ecological validity

The idea is that, in order to be ecologically valid, the entire set up of the study should closely approximate the real world scenario that is being investigated. In a sense, ecological validity is a kind of face validity. It relates mostly to whether the study “looks” right, but with a bit more rigour to it. To be ecologically valid the study has to look right in a fairly specific way. The idea behind it is the intuition that a study that is ecologically valid is more likely to be externally valid.

Confounder

A confounder is an additional, often unmeasured variable that turns out to be related to both the predictors and the outcome. The existence of confounders threatens the internal validity of the study because you can’t tell whether the predictor causes the outcome, or if the confounding variable causes it.

Artefact

A result is said to be “artefactual” if it only holds in the special situation that you happened to test in your study. The possibility that your result is an artefact describes a threat to your external validity, because it raises the possibility that you can’t generalise or apply your results to the actual population that you care about.

History effects

Refer to the possibility that specific events may occur during the study that might influence the outcome measure

Maturational effects

They relate to how people change on their own over time. We get older, we get tired, we get bored, etc

Repeated testing effect

A history effect in which the “event” that influences the second measurement is the first measurement itself!

Ex. If people are nervous at time 1, this might make performance go down. But after sitting through the first testing situation they might calm down a lot precisely because they’ve seen what the testing looks like.

Selection bias

Suppose that you’re running an experiment with two groups of participants where each group gets a different “treatment”, and you want to see if the different treatments lead to different outcomes. However, suppose that, despite your best efforts, you’ve ended up with a gender imbalance across groups (say, group A has 80% females and group B has 50% females). This is an example of a selection bias, in which the people “selected into” the two groups have different characteristics.

Homogeneous attrition

The attrition effect is the same for all groups, treatments or conditions.

Heterogeneous attrition

The attrition effect is different for different groups (often called differential attrition).

Non-response bias

You mail out a survey to 1000 people but only 300 of them reply. The 300 people who replied are almost certainly not a random subsample. People who respond to surveys are systematically different to people who don’t.

Regression to the mean

Refers to any situation where you select data based on an extreme value on some measure. Because the variable has natural variation it almost certainly means that when you take a subsequent measurement the later measurement will be less extreme than the first one, purely by chance.

Experimenter bias

The basic idea is that the experimenter, despite the best of intentions, can accidentally end up influencing the results of the experiment by subtly communicating the “right answer” or the “desired behaviour” to the participants.

Reactivity or demand effects

People alter their performance because of the attention that the study focuses on them

Placebo effect

It refers to the situation where the mere fact of being treated causes an improvement in outcomes. The classic example comes from clinical trials. If you give people a completely chemically inert drug and tell them that it’s a cure for a disease, they will tend to get better faster than people who aren’t treated at all. In other words, it is people’s belief that they are being treated that causes the improved outcomes, not the drug.

Data fabrication

Sometimes, people just make up the data. This is occasionally done with “good” intentions. For instance, the researcher believes that the fabricated data do reflect the truth, and may actually reflect “slightly cleaned up” versions of actual data. On other occasions, the fraud is deliberate and malicious.

Hoaxes

A hoax is often a joke, and many of them are intended to be (eventually) discovered. Often, the point of a hoax is to discredit someone or some field.

Data misrepresentation

It’s very common to see people present “aggregated” data of some kind and sometimes, when you dig deeper and find the raw data yourself you find that the aggregated data tell a different story to the disaggregated data. Alternatively, you might find that some aspect of the data is being hidden, because it tells an inconvenient story (e.g., the researcher might choose not to refer to a particular variable). There’s a lot of variants on this, many of which are very hard to detect.

Study “misdesign”

The issue here is that a researcher designs a study that has built-in flaws and those flaws are never reported in the paper. The data that are reported are completely real and are correctly analysed, but they are produced by a study that is actually quite wrongly put together. The researcher really wants to find a particular effect and so the study is set up in such a way as to make it “easy” to (artefactually) observe that effect.

Data mining & post hoc hypothesising

If you keep trying to analyse your data in lots of different ways, you’ll eventually find something that “looks” like a real effect but isn’t.

Publication bias & self-censoring

If 20 people run an experiment looking at whether reading Finnegans Wake causes insanity in humans, and 19 of them find that it doesn’t, which one do you think is going to get published? Obviously, it’s the one study that did find that Finnegans Wake causes insanity. This is an example of a publication bias. Since no-one ever published the 19 studies that didn’t find an effect, a naive reader would never know that they existed.

__Hentugleikaúrtak (convenience sampling)__

* Valið er í höndum rannsakanda.
* Þátttakendur valdir vegna þess að þeir voru á réttum stað og á réttum tíma fyrir rannsakanda.
* Dæmi væri stúdentar, fólk í Kringlunni.
* Ódýrasta aðferðin og tekur minnstan tíma.
* Auðvelt að nálgast þátttakendur.
* Miklar skekkjur og sjálfval þátttakenda.

__Matsúrtak (judgemental sample)__

* Valið er í höndum rannsakenda (sérfræðinga) og byggir á mati þeirra \n á því hversu rétt er að velja ákveðna þátttakendur fram yfir aðra.
* Oftast val út frá því hversu lýsandi þátttakandinn er fyrir þýðið.
* Þetta er ódýrt, þægilegt og fljótlegt en ekki hægt að alhæfa yfir á þýðið.

__Kvótaúrtak (quota sampling)__

* Kvótaúrtak er framlenging af matsúrtaki.
* Búum fyrst til flokka eða kvóta úr þýðinu út frá ákveðnum atriðum sem byggja á mati (kyn, aldur og kynþáttur).
* Kvótaúrtak tryggir að hlutfall atriða verði það sama og í þýðinu.  
* Getum notað hvaða aðferð sem er til að velja stök úr kvótunum.

__Snjóboltaúrtak (snowball sampling)__

* Veljum hóp af þátttakendum, oftast af handahófi, og biðjum þá svo um að benda okkur á aðra sem gætu tekið þátt í rannsókninni.
* Gott þegar verið er að vinna með eitthvað sjaldgæft.

__Einfalt handahófskennt úrtak (simple random sampling)__

* Hvert stak í þýðinu hefur þekktar og jafnar líkur á því að vera valið.
* (+) Er auðskilið og hægt að alhæfa yfir á þýðið.
* (-) Erfitt að setja saman úrtaksramma til að velja úr.  Úrtakið getur verið dreift yfir stórt svæði.

__Kerfisbundið úrtak (systematic sampling)__

* Við veljum ákveðinn byrjunarpunkt af handahófi og veljum svo hvert i stak eftir það.  Fjöldi er ákveðið með því að deila úrtakinu í þýðið (N/n).
* Hvert stak hefur þekktar og jafnar líkur á að vera valið.
* Ef röð á þýðinu þá minnkar svona úrtak á  alhæfingargildi gagnanna (t.d. Árstíðir, aldur eða stafrófsröð)

__Lagskipt úrtak (stratified sampling)__

* Tveggja þrepa ferli þar sem þýðinu er skipt upp í lög sem verða að vera þannig að hvert stak geti bara verið í einu slíku og ekkert stak vantar.
* Stökin eru lík en lögin eru ólík
* Stök eru síðan valin úr hverju lagi með tilviljun.
* Frábrugðið kvótaúrtaki þar sem stökin eru valin af tilviljun.
* Breytur til að skipta þýði í lög er t.d. lýðtölur, tegund viðskipta, stærð fyrirtækja, tegund iðnaðar.
* Lagskipt úrtak getur náð til undirþýðis (subpopulations) sem einfalt handahófskennt úrtak getur ekki alltaf.  Ef breytur skekktar þá gæti vantað í úrtakið mikilvæg stök t.d. tekjur.


* Lagskipt úrtak sameinar einfaldleika einfalds handah. úrtaks og möguleika á meiri nákvæmni.
* Dæmi um þetta gæti verið samkynhneigðir (5%). Ef ég vil fá svör frá þeim verð ég mögulega að taka sérstakt úrtak hjá þeim

__Klasaúrtak (cluster sampling)__

\n

* Skiptum þýðinu upp í klasa.
* Klasar eru líkir en stökin eru ólík
* Veljum klasa af handahófi.
* Notum annað hvort öll stök úr hverjum klasa (einna-þrepa klasaúrtak) eða drögum úr þeim af handahófi (tveggja þrepa klasaúrtak).
* Munur við lagskipt úrtak er að í klasaúrtökum notum við aðeins hluta af undirþýðunum.
* Dæmi: Setjum skóla í klasa (1/3 góðir, 1/3 lélegir og 1/3 miðlungs skólar).  Veljum af tilviljun klasa
* Markmiðið með klasaúrtaki er úrtaksskilvirkni (efficiency) en í lagskiptu úrtaki er að auka nákvæmni.


* Stök í klasaúrtaki eiga að vera ólík en klasar líkir en í lagskiptu úrtaki eiga stök að vera lík en lögin ólík.
* Svæðisúrtak er eitt helsta form klasaúrtaka.
* Helstu kostir:  Þægilegt og lítill kostnaður.  Oft aðeins til klasar þegar verið er að skoða úrtaksramma.
* Gallar:  Frekar ónákvæm aðferð og erfitt að búa til klasa með ólíkum stökum vegna þess að fólk er oft svipað í hverfum eða götum.  Erfitt getur verið að reikna úr og túlka niðurstöður.

Staðalfrávik

Ef ég er með meðaltalið og skoða síðan meðaltals fjarlægð allra punkta frá meðaltali og það er staðalfrávikið.

Meðaltal

Einfalt meðaltal, algengasta mæling á miðlægu gildi, algengasta mæling á miðlægni. Meðaltal = Summa mælinga deilt með fjölda.

Miðgildi

Tala í safni þar sem jafn margar tölur eru hærri og lægri. Í gögnum sem er raðað frá lægst til hæsta gildi, miðgildi er tala í “miðju” (50% lægri og 50% hærri).

Tíðasta gildi

Tala sem kemur oftast fyrr. Ein vísbending um miðlægni. Tala sem kemur oftast fram í gagnasafninu. Öfgagildi (outliers) hafa ekki áhrif á niðurstöðu. Notuð bæði fyrir talnagildi og flokkunargögn. Stundum er ekkert tíðasta gildi. Stundum eru fleiri en eitt tíðasta gildi.

Óháð breyta (frumbreyta)

Orsök (cause)

Áreiti

Hefur áhrif á háðu breytu

Háð breyta (fylgibreyta)

Afleiðing (effect)

Svar

Þýði

Allir sem við höfum áhuga á

Úrtak

Hluti af öllu í þýðinu

__Kostir tilrauna__

* Möguleiki rannsakandans til að hafa áhrif á óháðu breytuna
* Einangrun frá utanaðkomandi breytum (exogenous variables) er auðveldari
* Kostnaður og umstang er yfirleitt lítið
* Endurtekning með misjöfnum hópum og skilyrðum
* Rannsakendur geta notað vettvangsrannsóknir

__Gallar tilrauna__

* Tilraunastofur eru oft gervilegar
* Alhæfingar út frá úrtaki sem ekki er dregið af tilviljun geta leitt af sér vandamál. 
* Sumar tilraunir mjög dýrar (t.d. tilraunir á hjálparstarfi)
* Tilraunir passa best á spurningar um nútíð en eiga erfiðara með spurningar um fortíð eða framtíð
* Það eru takmörk fyrir því hvað sé siðferðilega réttlætanlegt í tilraunum