PSYC 203 1st Edition Lecture 1 Outline of Last Lecture I. Introduction to course Outline of Current Lecture II. Parameters and StatisticsA. Definition of eachB. ExamplesIII. NotationA. MeanB. Summation NotationIV. Sampling errorA. DefinitionB. ExamplesV. Types of VariablesA. Discrete B. ContinuousVI. HistogramsA. DefinitionVII. Central TendencyA. 3 measures of central tendency Current LectureParameters and Statistic- A numerical value that describes a population is called a parameter.- A numerical value that describes a sample is called a statistic. o Example: Assume that the average extraversion score for all women in the USA is 3.5. This is a parameter, with the population being all the women in the USA o The average Extraversion score in a sample of 155 is 3.42. This is a statistic, with the number taken from 155 women out of all of the women in the USA. o An easy way to remember this is that both parameter and population start with “P” and both sample and statistic start with “S”Notation- Specific notations used in psychology statistics include:These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.o N= # of scores in a population o N= # of scores in a sample  Example: The mean , or average (the sum of all the scores divided by the number of scores in the data)  Population Mean μ= (Σχ)/N Sample Mean μ= (Σχ)/no Summation notation  Many statistical procedures require you to add up a set of scores. The summation sign Σ stands for summation- It is always followed by a symbol or equation that defines what is to be summed - To remember the order of operations just recall “Please Excuse My Dear Aunt Sally” (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)- Preview- Sum of Squares (SS)o Find each deviation score (χ-μ)o Square each deviation score, (χ-μ)^2o Sum up the squared deviations  SS=Σ(χ-μ)^2- Sampling Error o The discrepancy between a sample statistic & its population parameter is called sampling error. Addressing concerns about sampling error is a large part of inferential statistics. o We will be dealing with random errors that create differences between statistics and parameters.Example: x= Σx/n = 18.9/5 Example of The United States’ murder rates 4.4, 2.9, 3.9, 2.7, 5.0 (took score of a 5 states)18.9 comes from the sum of the above listed numbers N=50 (the 50 states)The 5 comes the 5 examples we took (4.4, 2.9, 3.9, 2.7, 5.0)μ=4.7x=3.78 the sampling error can be found because μ4.7 & x=3.78 aren’t the same numbers o Addressing concerns about sampling error is a large part of inferential statistics o We will be dealing with the random errors that create differences between statistics and parameters?o Example of sampling errors  Population mean is 4.26 (N=50) Draw 5 random samples of 10 observations from this populations (n=10) take the average from each sample  3.92, 4.78, 4.59, 3.76, 3.96o Another example: What if I lived in New Hampshire and can only sample neighboring states?  State 1 1.1 State 2 1.3 State 31.9 State 41.8 Mean = 1.52 - 6.1/4=1.52 (according to formula: M= Σx/n)- this example wouldn’t classify as a random error becausewe selected states that specifically neighbor NewHampshire - Inferential Statisticso Allow one to start with sample data and make general conclusions(inferences) about populations.o One can make statements about how likely(or unlikely) a sample came from a certain population. o Given a ‘good study’ larger samples sizes(i.e., more data) usually lead to more confident inferences.... o Golden Rule of Sample Size=Bigger is Better! - Types of variableso Continous & discrete o Continuous variables are infinitely divisible into whatever units a researcher may choose. Ex: how attractive is person xo Discrete (or categorical) consist of a finite number of categories. Ex:democrat/republican/independent - Histograms o allow us to see the distribution of data. The height of each bar is the number of times each value occurs in the dataset. Distributions can vary in 4 ways- Central tendency–- Variability– - Skewness- Kurtosis- Central Tendency o Single value that accurately describes the center of a distribution of scores o Some sort of average of “typical value”o What single value best represents an entire set of scores? Use mean, median, mode  No single one is always the best one  The mean is the most commonly used - Conceptually, the mean can also be thought of as:o The amount that each individual receives when thetotal (ΣX) is divided equally among all individuals. o The “balance point” of the distribution because the sum of the distances below the mean is exactly equal to the sum of the distances above the mean.  Changing the mean: - Changing the value of any one score will change the value of the mean - Adding or removing scores will also change the value of the mean - Adding a constant to every score increases the mean by that constant. o Ex.: 3 + 6, 4 + 6, 8 + 6_M = (9+10+14)/3 = 5 + 6 = 11 - Multiplying each score by a constant results in the mean being multiplied by that constant o Ex.: 3 * 3, 4 * 3, 8 * 3_M = (9+12+24)/3 = 5 * 3 =