Introduction to Statistics in Psychology PSY 201 Professor Greg Francis VARIABLES DEPENDENT VARIABLES factors that affect data e g variables might include study the effect viewing violent video games on childhood aggression Lecture 02 number of violent acts in game age of child time spent playing the game time sense last played the game measurement scales frequency of play descriptive statistics other activities What is our national security threat gender of child number of friends aggressive acts by the child You might want to measure many different variables 2 3 DEPENDENT VARIABLES VARIABLES INDEPENDENT VARIABLES these are the variables that measure the effect you are interested in researchers are interested in how dependent variables change as other variables change see how the dependent variables depend on other variables two types number of violent acts in game age of child time spent playing the game time sense last played the game frequency of play other activities gender of child other variables are called independent variables researcher either keeps track of or controls the values of independent variables number of friends 1 researcher manipulates variable e g have children play a video game for various durations and measure the effect on aggression 2 variable classifies e g gender age of child study wants to know how the dependent variable changes with changes in the independent variables aggressive acts by the child these measurements are not always easy to get 4 5 6 LEVELS OF VARIABLES independent variables can have different levels e g gender of child 1 male CONFOUNDING VARIABLES some types of independent variables are present but not really related to a study For example a child s tendency to play a violent video game may be related to aggression in the family 2 female time spent playing video games 1 0 1 hours per week 2 2 5 hours per week 3 6 10 hours per week 4 11 20 hours per week 5 more than 20 hours per week socioeconomic status weather availability of counseling a researcher often cannot manipulate these variables ethics EXAMPLE let s identify the dependent variable independent variable and possible confounding variables A researcher wants to know the effect of sweetener sweetened unsweetened added to drinking fluid on the amount of fluid drunk by subjects A researcher wants to know the effect of type of counseling group individual on clients level of emotional adjustment a researcher can sometimes control for these variables by measuring them and insuring effects do not depend on them 7 8 9 MEASUREMENT NOMINAL SCALE NOMINAL SCALE studies need to identify variables and measure them classification of objects into categories two key properties different variables have different scales of measurement four scales of measurement least precise to most precise nominal ordinal e g nationality color of eyes 1 data categories are mutually exclusive 2 data categories have no logical order gender numbers can designate categories names of objects 1 blue eyes 2 brown eyes 3 green eyes no order to the categories interval but the order of numbers does not imply order of categories because there really is no order ratio 10 11 12 ORDINAL SCALE ORDINAL SCALE ORDINAL SCALE ordered classification numbers can be used to designate categories e g finish in a race but size of number does not correspond to amount of relevant characteristic e g grading system A B C D F warmth cold cool warm hot 1 first place 2 second place finish in a race 3 third place order is important and means something 4 fourth place the difference between fourth and fifth might be much larger than the difference between first and second Olympic Men s 100m Butterfly Finals order of numbers agrees with order of categories 13 14 15 ORDINAL SCALE ORDINAL SCALE USING SCALES but size of number does not correspond to amount of relevant characteristic characteristics One needs to pick items that have a natural scale to convey certain types of information the difference between fourth and fifth might be much larger than the difference between first and second Olympic Men s 100m Butterfly Finals 1 Michael Phelps 50 58 s 2 Milorad Cavic 50 59 s 1 data categories are mutually exclusive 2 data categories have some logical order 3 data categories are scaled according to the amount of the particular characteristic they posses 3 Andrew Lauterstein 51 12 s this makes them a poor choice for labeling of ordinal data because people do not automatically know what the different colors mean this is a problem for the National security warning system which uses colors to indicate different terrorist threat levels 4 Ian Crocker 51 13 s 5 Jason Dunford 51 47 s 6 Takuro Fujii 51 50 s 7 Andrii Serdinov 51 59 s Which is more severe green threat or blue threat 8 Ryan Pini 51 86 s 16 Thus for example colors are typically at the nominal scale of measurement 17 18 MATCHING SCALES INTERVAL SCALE INTERVAL SCALE equal unit scale numbers can be used to designate categories e g e g temperature Fahrenheit or Celsius IQ scores try to be most tests 25 F level of heat 28 F level of heat no beginning to scale the problem is that the scales of terrorist threat ordinal 22 F level of heat zero point is just another category scale and color nominal scale do not match Thus order of numbers agrees with order of categories number differences agree with characteristic differences e g 3 F news reports of the terrorist threat level invariably do not list only the color but also the associated phrase with each report The color scale is of no use at all 19 20 21 INTERVAL SCALE INTERVAL SCALE WHY ZERO MATTERS zero point 0 temperature does not mean no heat in F and C I can create an equivalent interval scale that preserves all the differences NEWIQ OLDIQ 20 0 IQ does not mean no intelligence differences are still the same 50 IQ 100 IQ 150 IQ an adult with a 50 IQ should have 50 fewer units of intelligence than a person with a 100 IQ a person with a 100 IQ should have 50 fewer units of intelligence than a person with a 150 IQ 50 F IS not twice as hot as 25 F an IQ of 100 is not twice as smart as an IQ of 50 100 120 50 70 but the ratios are all different 170 is not 1 5 times 120 Multiplication makes no sense however you cannot say that a genius 150 IQ is 1 5 times as intelligent as an average 100 IQ 22 150 170 if zero meant absence of trait I could not create an equivalent interval scale zero would have to correspond to zero and nothing else 23 24 INTERVAL SCALE RATIO