Unit 1 The structure of Data Population The set of people animals groups etc that we are interested in studying Example If my research is about the behavior in first time mothers my population would be all mothers between flies and mosquitos the population is Clicker Question And if I want to know whether frogs can tell the difference A flies B mosquitos C people D frogs Remember the group we are interested in studying in this case it would be the frogs The problem is it is almost impossible to study the whole population Its would be impossible to study for example every single frog In the real world we can only study a subset of the population Sample Subset of the population The Sample in some cases can be very small The Size of the sample will depend on practical consideration such as Cost of the study If it cost 500 to study each individual you can expect for the sample to be fairly small How hard is it to find members of the population For example if your population consist of color blind Children between the ages of 3 6 It would be rather difficult to find a large sample of this population therefore the population would be represented by a small sample But even a large sample is usually really really small relative to the size of the population Random Sample sample is to be chosen at random from the population A random sample is just a set of members of the population selected in such a way that all individuals in the population have an equal chance of being in the sample Example Give each member of the population a number and let the computer decide which members get to be part of the sample But this too would be impossible How could you possibly give a number to EVERY individual of the population You don t In practice sample are never really random Sample of convenience Members of the population that are easy to find The important part is to find individual that are representative the population What it means is that the members of the population that end up in our sample are likely to be similar to the population as a whole at least with respect to the things that matter for our study Branches of Statistics Descriptive Statistics Describes data from sample Inferential Statistics Use the data from our sample to draw inferences about the larger population from which the sample was drawn In practice the order of things is like this first we collect some data from a sample then we use descriptive statistics to summarize these data then we use inferential statistics to draw inferences about the population from which the sample was drawn Some Terminology Individuals The things we are measuring which make up our sample Individual does not necessarily mean people it depends on the research on question it could be animals cells etc Variables The properties of the individuals that we are interested in Example height weight gender etc Values are what we call the various values that the variable can have Data Set When we have a collection of values of variables for a set of individuals Data frame The data set that is organized in a table in R Example Year Sex education Vocabulary 20040001 2004 Female 9 3 20040002 2004 Female 14 6 20040003 2004 Male 14 9 20040004 2004 Female 17 8 each row is an individual Each column is a variable The number and the words in table itself are the values Variables Quantitative Variable or Numerical Variable is something that has numbers as values Example Height age cholesterol Categorical Variable variable is something that does NOT have numbers as values Example Hair color ethnicity Clicker Question Which of the variables in this data frame is categorical A year B sex C education D vocabulary Categorical question could be disguised as numerical ones When thinking about whether a variable is really categorical or numerical you have to think about whether the values can be thought of as representing quantities If they can the variable is numerical If not it is categorical Within the class of numerical variables there are two kinds continuous and discrete Quantitative Variables Continuous Variable can take any numerical value Discrete Variable can take only certain values not the ones in between Example You have two siblings It is not possible to have 2 5 siblings Clicker Question Which of the variables in this data frame is truly a discrete numerical variable A type B price C driveTrain D passengers it is impossible to have 1 5 passengers Therefore it is truly a discrete numerical variable Quantitative variables can also be measured in three types of scales Ordinal Scale the values can only be interpreted in relative terms Example 5 is higher than 3 which is higher than 1 You can t interpret the values themselves as having any specific meaning Quantitative Variable Interval Scale Difference between scores of a given amount always mean the same thing Example If it is 60 F on Monday 70 F on Tuesday and 80 F on Wednesday then the difference between Monday and Tuesday really is the same as the difference between Tuesday and Wednesday Ratio Scale you can interpret the differences between values and in addition there s a meaningful zero point Example how much money do you have in your pocket Clicker Question Which of these variables is on an interval not ratio scale A distance in miles B time of day on a 12 hr clock Same amount of lapse each time and has no meaningful zero C years of education D right vs left handedness temperature in Celsius interval Clicker Question Which of these variables is on a ratio scale A B U S News rankings of colleges ordinal C age of fruit flies in days It is sometimes necessary to transform data from one unit to another Example you might want to convert height measured in feet to height measured in inches With a linear transformation you multiply or divide by a constant and or add or subtract a constant In a liner transformation all relationships between values are preserved Non linear transformations do not have this property