Samenvatting
Statistics summary
- Vak
- Statistics
- Instelling
- Radboud Universiteit Nijmegen (RU)
Statistics Summary, Field, CH: 1-4, 8,10, 12, 19
[Meer zien]Voorbeeld 4 van de 46 pagina's
Voorbeeld 4 van de 46 pagina's
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StatisticisChapter 1
Theorieis: a hypotheisized general priniciple or iset of prinicipleis that explain known fndingis about a
topiic and from whiich new hypotheiseis ican be generated.
Hypotheisiis: a teistable prediicton.
Falisificaton: diisproving a theory or hypotheisiis.
Variable: anything that ican be meaisured and ican difer aicroisis entteis or tme.
Typeis of data analyisiis
Quanttatve: teistng theorieis uising numberis > istatisticis
Qualitatve: teistng theorieis uising language, e.g. interviewis, newispaperis, media.
Typeis of hypotheiseis
Null hypotheisiis H0: when there iis no relatoniship between two meaisured phenomena, or no
aisisoiciaton among groupis. > no diferenice (whiich iis what you want to diisprove..
Alternatve hypotheisiis H1: when you expeict an efeict. (Aliso icalled Ha..
How to measure p13
Correlatonal reisearich: obiserving what naturally goeis on in the world without direictly interfering
with it. >temptaton iisland example from leicture.
>istatementis about icauisaton icannot be made.
Experimental reisearich: when we manipulate one variable to isee itis efeict on another.
>istatementis ican be made about icauise and efeict.
Experimental reisearich methodis
Cauise and efeict:
>muist oicicur icloise together in tme (icontguity..
>icauise muist oicicur before the efeict doeis.
>an efeict ishould never oicicur before the icauise.
Confounding variableis (Tertum Quid.: when another variable (not the one prediicted. hais an efeict
on the outicome.
Methodis of data icolleicton p15
Between-group/isubjeict/independent: diferent entteis in experimental iconditonis.
Within-isubjeict/interdependent/repeated meaisureis: when the isame entteis take part in all
experimental iconditonis.
>advantage: eiconomiical (fewer participantis are needed., more isenisitve to deteict efeictis.
>diisadvantage: praictice efeict, boredom, potental inisightis into experimenter is goal.
Praictice efeict: when teist participantis may perform diferently in the iseicond iconditon due to
familiarizaton.
Boredom efeict: when participantis perform diferently the iseicond tme due to being
bored/tred from the frist teist.
Typeis of variaton p16
Syistematic variaton (efeict.: difereniceis in performanice icreated by a ispeicific experimental
manipulaton.
Unisyistematic variaton (noiise.: difereniceis in performanice icreated by unknown faictoris, e.g.: age,
gender, IQ, tme of day, + meaisurement erroris.
,Randomizaton and icounterbalanicing > minimizeis unisyistematic variaton.
Randomizaton: mixing the groupis, e.g. motvatonal and other istudentis in two equal groupis.
Counterbalanicing: the order in whiich a perison participateis in a iconditon. (for within isubjeict deisign..
What to measure? Independent and dependent variableis p7
Independent variable: the variable that we think iis a icauise, aliso Prediictor Variable.
>beicauise itis value doeis not depend on any other variableis.
>it iis the manipulated variable (in experimentis.
Dependent variable: the value of thiis variable dependis on the icauise, aliso Outicome Variable.
>it iis the propoised efeict.
>meaisured not manipulated (in experimentis.
Levelis of meaisurement p8
Categoriical: when entteis are divided into diistnict icategorieis.
1. Binary variable: only two icategorieis, e.g. dead vis alive, paisis vis fail.
2. Nominal variable: more than two icategorieis, e.g. omnivore, vegetarian, vegan, or
fruitarian.
3. Ordinal variable: nominal variable with icategorieis in a logiical/ichronologiical order.
Contnuouis: when entteis get a diistnict order.
1. Interval variable: equal intervalis on the variable repreisent equal difereniceis in the
property being meaisured, e.g. diferenice between 6 and 7 iis equal to the diferenice
between 8 and 9.
2. Raton variable: the isame ais an interval variable, but the ratois of isicoreis on the isicale
muist make isenise, e.g. a perison with a isicore of 80 on a teist hais reisponded icorreictly to
twiice ais many queistonis than a perison with a isicore of 40.
Meaisurement error: the diisicrepanicy between the aictual value we re trying to meaisure, and the
number we uise to repreisent the value. P11
Validity and reliability p12
Validity: whether an inistrument meaisureis what it iset out to meaisure.
1. Criterion validity: the degree to whiich a teist aictually meaisureis behaviour.
>Conicurrent validity: when there iis a icorrelaton with another validated inistrument.
>Prediictve validity: the extent to whiich a isicore on a isicale/teist prediictis isicoreis on
isome icriterion meaisure.
2. Content validity: evidenice that the icontent of a teist icorreispondis to the icontent of the
iconistruict iis wais deisigned to icover.
3. Eicologiical validity: evidenice that the reisultis ican be applied, and allow interfereniceis, to
real-world iconditonis.
Reliability: the ability to produice the isame reisultis under the isame iconditonis.
Teist-Reteist reliability: the ability of a meaisure to produice iconisiistent reisultis when the isame entteis
are teisted at two diferent pointis in tme.
>a meaisure iis not valid if not reliable.
,Analysing data
Frequenicy diistributon aka Hiistogramis: a graph plotng valueis of obiservatonis on the horizontal axiis,
with a bar ishowing how many tmeis eaich value oicicurred in the data iset.
Normal diistributon: bell ishaped; isymmetriical around the icentre.
Properteis of frequenicy diistributonis p19-21
Skew: hais to do with the isymmetry of the diistributon.
1. Poisitve iskew: isicored buniched at low valueis with the tail pointng to high valueis
2. Negatve iskew: isicoreis buniched at high valueis with the tail pointng to low valueis.
Kurtoisiis: hais to do with the heavineisis of the tailis, and the pointneisis of diistributon.
1. Leptokurtic = heavy tailis and pointy.
2. Platykurtic = light tailis and rounded. (remember “plat”.
Mode, median, mean p21-24
Central tendenicy: icaliculatng where the icentre of a frequenicy diistributon lieis.
Mode: the moist frequent isicore.
-two more variatonis: bimodal and multmodal.
>diisadvantageis: mode ican have iseveral valueis, and it ignoreis moist of the isicoreis.
Median: the middle isicore when isicoreis are ordered.
>diisadvantage: ignoreis moist of the isicoreis.
Mean: the isum of isicoreis divided by the number of isicoreis.
-when the data are very iskewed, median and mode are preferred over mean.
>diisadvantageis: afeicted by extreme isicoreis, icannot be uised for nominal/ordinal data. BUT it
doeis uise every isicore, and it tendis to be istable in diferent isampleis.
Range p24
Range: ismalleist isicore isubtraicted from the largeist, e.g. higeist: 234; loweist: 22, range= 234 22 = 212
p24
> diisadvantage: highly afeicted by isudden extremeis.
The interquartle range (IQR.: the 3 valueis that isplit isorted data into 4 equal partis.
Diferenice between upper and lower quartle = IQR.
>diisadvantage: ignoreis half of the data.
Other quartleis ican be Pericentleis (isplitng data into 100 diferent partis., and Nonileis (isplitng data
into nine equal partis..
Devianice p25
If we uise the mean ais a meaisure of the icentre of a diistributon then we ican icaliculate the diferenice
between eaich isicore and the mean, whiich iis known ais devianice.
individual isicore mean
if we want to know the total devianiceis we icould add up the devianiceis for eaich data point.
, > meanis “add up all of what icomeis afer”.
Sum of isquared erroris, SS(e. p26
Thiis indiicateis the total diisperision of isicoreis from the mean:
“Squared” meanis tmeis itiself (e.g. devianice of 73 > 73*73..
SS(e. = all isquared devianiceis added.
>diisadvantage: isize dependis on nr. of isicoreis in data.
>more uiseful would be average diisperision (varianice., inistead of TOTAL diisperision:
= all isquared devianiceis added / by the nr. of obiservatonis.
THEN we want to take the isquare root of the varianice, whiich iis known ais the istandard deviaton.
Why?: the varianice giveis uis a meaisure in unitis isquared. P27
Important to remember
The isum of isquareis, varianice, and istandard deviaton repreisent the isame thing: the variability in the
data, error, the ft of the mean to the data, how well the mean repreisentis the obiserved data.
Uising a frequenicy diistributor to go beyond the data
For any diistributon of isicoreis, we icould, in theory, icaliculate the probability of obtaining a isicore of a
icertain isize (doeisn t happen ofen, but we icould.. Statisticianis have identfed iseveral icommon
diistributoris. For eaich one they worked out mathematical formula, known ais probability denisity
funictonis. They ispeicify idealized verisionis of theise diistributonis. We icould draw isuich a funicton by
plotng the value of the variable (x. againist the probability of it oicicurring (y.. The reisultng icurve iis
known ais a probability diistributon.
Z-isicoreis (important) p31
Z= eaich isicore (x = mean. mean of all isicoreis / istandard deviaton.
It expreisiseis a isicore in termis of how many SD is it iis away from the mean.
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