See answer: nd the partial-fraction decomposition for each rational function

100B Monday Lecture Week 2 - You had to do 100B work over the weekend - Hypothesis: testable prediction - Correlation: two variable are correlated (part of hypothesis) - If we find out that these two variables are correlated we can make predictions o But we cannot apply causation because  Third variable problem  We don’t know directionality (which causes which) o We can’t apply causal claims - Example: coffee consumption and fertility are correlated o Of women trying to get pregnant, women who drank more than three cups of coffee per day take at least more than a year to conceive. o Predictor variable: amount of coffee that women drink per day o Criterion variable: the time it took these women to conceive o X axis: predictor variable: amount of coffee o Y axis: criterion variable (months) o this is a positive correlation. Use scatterplot whenever you plot correlations o third variable could be lack of sleep o third variable could cause increase in both variables o or taking longer time to conceive could cause coffee o criterion variable can cause predictor variable - it would be useful to make causual conclusions o (we would have to eliminate directionality and third variable issue) o We would need to perform new studies o In order to say A causes B, we need to manipulate A o By manipulating A, we need to control everything in the situation and control A o A is independent variable - Independent variable o Manipulate  by controlling evyerhting else (dependent variable) - Dependent variable o Measure - Experimental design: manipulating independent and measuring dependent o True experiment: actually manipulating independent - Does watching violent TV cause aggressive behavior o We need to manipulate independent variable o Manipulate violent TV and see if that affect dependent variable  How  Tell children how much violent tv to watch  Random assignment: randomly assign each child to different level of IV (different amount of TV)  Violent tv/aggressive behavior are constructs  Operational definition: take a construct and define that construct o Define interference and discrete task o Totally up to us how we define construct o Operation definition up to us  Interference defined: how long it takes Independent Variable o is number of hours children watch TV o At least 2 levels o Randomly assign children into those two level o Can be manipulate quantitative or qualitative o Quantitative: how much is the difference o Qualitatively: type of violent TV  One group watches violent drama, one violent show etc  IV for our experiment o We will use quantitative (effect of amount of TV) o X axis: independent variable: amnt violent tv o Might find that watching violent TV increases aggressive behavior might decrease aggressive behavior, or it might stay the same o By adding a third level: we can get a lot more information  Adding third level o Turns into functional relationship, not linear o Range is really important  If you found that there is no difference in aggressive behavior with change in minutes, that wouldn’t be sound conclusion if range wasn’t big enough (you did 0, 5, 10 minutes)  IV changed to type of violent TV  Aggressive behavior vs type violent TV  Use bar graph when IV is qualitative (use line graph when it’s quantitative)  Our experiment  Operationally define IV: only thing that is different is amount of tv watched  Everything else is controlled  Put more specifics on it - Types of measurement that we have o We now need to operationally define our dependent variable o Different types of measurements  self report: when you are asking someone to report on themselves  ex: how aggressive are you  not always accurate  behavior measures: behavior  watching them and measuring them  ex: number of times a kid hit another  physiological: anything from your body  ex: blood pressure - Types of scales o Different scales  Nominal: often “yes” or “no”  Ex: aggressive or not  Ordinal: categories with an order!  Ex: first place, second place, third place  Ex: not, somewhat, very  Although we can order them, the magnitude between them is not constant or equal  Interval: differences are constant or equal  Ex: rate 5-15 o These are all arbitrary  Ratio:  0 matters; means there I an absence of whatever you’re measuring  Not ex: A 0 on an IQ test does not mean that there is an absence of what you’re measuring  Ex: time, weight - We need to think about o Reliability and validity  Reliability: consistency of our measures  Example: whether or not a drug makes a rat go through a maze faster  Types of reliability  Test- retest: test yourself and then test yourself again, tests reliabilty  Interrater: judges, must be consistent with eachother o If they are not consistent, then low interrater reliability  Replicability: imagine that your results are pulished and someone wants to replicate your study o If your results aren’t replicable and people can’t get those results again then your results are going to be discounted  Validity: are your measures measuring what you say they are  Accuracy  Something can be reliable without being valid or vice versa  Types o Construct validity: also called “face”: how well your operational definition represent your construct  Ex: poor construct validity: if you use yawning to understand how smart you are o Internal validity: checks the integrity between the causual relationship between independent and dependent  Measures whether the manipulation of IV really casues DV  We need high internal validity  Ex: you want to be able to say IV causes DV.  Extraneous variable: something that would be causing the DV that’s not the IV  We must control everything (extraneous variables) so that they can’t penetrate IV-> DV relationship  Confounding variable: extraneous variable that varies systematically with the levels of the IV  How to increase internal validity  Controlling extraneous variables o External validty: how well does your study represent what happens in the real world  Low external validty: does not represent what is happening in the real world o Biggest issues  Dance between internal and external validity  Depends on your research question which is more important  You hope for perfect balance between the two o Review  First thing is to figure out IV  Operationally define it o First question: quant or qual  Qualitative; 3 levels: news, cartoon, crime show o All need to watch tv  Random assignment to condition  Put specifics on it  Control extraneous variables  DV  Aggressive behavior  Type: behavioral o Number of punches: ratio (difference beween each punch is different) o =