Statistics of Psychology PSYCH 301 – 1st EditionExam # 1 Study Guide Lectures: 1 - 5Lecture 1 (January 12)Describing Datai. Different types of variables- Relevant variables:o Independent variables / IV / predictor variables (what you manipulate)o Dependent variables / DV / outcome variable (what you’re measuring)- Values:o All variables can take on different values (gender, memory span, etc.)o A persons value on a variable is called a score- Score:o One individuals value/scoreii. Kinds of variables:- Nominal: categories, names, gender, species, etc.o Discrete : only certain values are possible (values that are cut and dry)- Ordinal (rank order): relative ranking; variables with values that can be organized.(Year in college, class rank, etc.)- Interval (equal-interval): numbers; age, height, weight, etc.o Continuous: within this range, mostly any valuable is possible.- Ratio: an interval that can include a zeroiii. Graphs:a. Frequency table: a table filled with frequency; how often does each score happen?b. Grouped frequency table: how often does each score happen in the groups of the dependent variable c. Histogram: displays the frequency of different valuesi. x-axis: DV (continuous), y-axis: frequencyd. Bar Chart: relating the dependent variable to the independent variable i. x-axis: IV (discrete), y-axis: DV (continuous)e. Line Chart: x-axis: IV (continuous), y-axis: DV (continuous)f. Scatter plot: each dot is a collection of two different variablesi. x-axis: IV (continuous), y-axis: DV (continuous)iv. Distributing Data:a. The first step in all data analysis is finding the shape of the distribution of data.i. Bell-Shaped Curve, Positive Skew, Negative Skew, Multimodal, OutliersLecture 2 (January 14) Central Tendency & VariabilityI. SUMMARIZING THE DATA (STEPS)1) Find out the shape of the distribution (Make a histogram)2) Quantify the center of the distribution (mean, median, mode)3) Quanitify the spread of the distribution (Range, standard deviation, variance)II. CENTRAL TENDENCIES a. MEAN: The average: add up all scores and divide by n. (the number of scores)b. MEDIAN: The middle of the data set when arranged from lowest to highesti. If data set has an even number of data points, you take the average of the2 numbers closest to the middlec. MODE: Most frequently observed data point (may by more than one number)d. RANGE: The largest value minus the smallest valueIII. SUMMERIZING THE DATA : CENTERa. A distribution of data can only have 1 mean and 1 medianb. A distribution of data can have many modes, up to the number of n’sc. The mean is most appropriate for interval datad. The median can be applied to ordinal or interval datae. The mode can be applied to interval, ordinal, or nominal dataf. In a histogram, when data are symmetric and unimodal, the mean, median, and mode are very close to one another at the center.i. when distributions are skewed, the mean, median, and mode spread outg. Means are strongly affected by outliers, the medians and modes are not. h. Sometimes the means don’t tell the whole story. You could have one data set where everyone’s scores were within a range of 3, and one set where the scores have a range of 13, with the means being the sameIV. SUMMARIZING THE DATA: SPREADa. Standard Deviation (SD) measures the average deviation from the mean value- “average”: add something up and divide by n- “deviation”: (difference) subtract two numbers- “deviation from the mean”: subtract scores minus the meanii. the deviation is squared because if you didn’t square the deviation from the mean, you would always end up with a sum of zeroiii. the square root undoes the squared deviation- x: one data point- : the mean of the data points- : the sum- n: the total number of scores (x)iv. STEPS:1) calculate the mean2) take each score and subtract the mean3) square each deviation4) add all deviations up5) divide by n 6) take the square root b. Variance measures the average squared deviation from the mean value. (Larger deviations indicate greater spread.)- Variance has the same steps as SD, except taking the square root in step 6.- ( √var = SD / SD² = Var )ii. STEPS:1) calculate the mean2) take each score and subtract the mean3) square each deviation4) add all deviations up5) divide by n 6) take the square rootLecture 3 (January 21)Measuring ProbabilityV. Probability – “What are the odds of X happening?”a. Expected relative frequency of a particular outcomei. Outcome: one of the events that could happenProbability =Possible Successful OutcomesAll Possible OutcomesVI. Probability vs. PercentageProbabilities PercentagesP x %0 ≤ p ≤ 1 0% ≤ x ≤ 100%Never Negative! Never Negative!Sum to 1 Sum to 100%VII. Measuring Probability i. List or count all possible outcomesii. How many different ways are there of achieving an outcome?1. Sometimes there is only one way, other times there are manyiii. What is the outcome of interest?VIII. Random Sampling- Law of Large Numbersa. This does not mean that the outcome is unpredictableb. Random processes usually produce highly regular resultsc. Nonrandom processes won’t be representative of the populationd. The Probability of a random outcome can be estimated by the proportion of times it happens in a very large number of trialsIX. Calculating Probability (3 ways)1. Independent Trials: when the outcome of one trial does not affect the outcome of the next.- The Probability of your outcome will never change2. Histograms show all possible outcomes. All outcomes have a probability that sumis equal to 1 / The sum of all probabilities in a histogram equals 1.- We can use a histogram to find out the probability of some particular events happening.Lecture 4 (January 26)Z ScoresI. Knowing both the mean and standard deviation (or variance) allows us to compare one score to the populationa. Symbols: Sample vs. PopulationSamplestatisticsPopulationsscoresMean M μStandard Deviation SD σVarience SD² σ²Greek letters mean the data is talking about populationb. Normal Distribution is controlled by 2 parameters: i. Mean (location) and Standard Deviation (width) -3 -2 -1 0 1 2 3II. Z Score: transforming a raw score into a standard score. (can only be used with bell-shaped data)a. Clarifies the relationship between one score and the rest of the data. (how far away from the mean is this score?)b. Difference from the mean/ variabilityc. There are 2 equal equations. The difference is who we are