PSY 207 notesINTRO-Sampling error: discrepancy between the sample statistics and the population parameter is sampling error-Data: collection of numerical observations from a survey/experiment (single datumm is called raw score)Quantitative vs. Qualitative Data-Qualitative data: (always discrete data) single observation, which represents a class or categoryQuantitative Data : (not always continuous) A single observation is an amount or a countDiscrete vs. Continuous Data-Discrete: countable number of possible values (ex. # cars in parking lot)-Continuous: infinite number of possible values on a scale in which there are no gapsor interuptionsExperimental Design***Importance in Random Assignment-Variable: A characteristic or property of organisms, events, or objects that can take on different values-Constant: characteristic/property that doesn’t change-Independent Variable: manipulated by the investigator-Dependent variable: variable measured by the investigatorQuasi-experimental (non experimental)-cases where researcher has no control ofgroup assignment-inability to rigorously control for extra-neous variablesCorrelational Study-investigator measures two DV’s and looksfor relarionship-REMEMBER: correlation doesn’t determine causationScales of Measurement1. Nominal: refers to data that consists of names, labels, categories2. Ordinal: refers to data or scores that can be arranged in some order (give us rank order. ex. 1st, 20th, etc.)3. Interval: refers to data that have meaningful differences between scores. Tells us identity and rank order-Equidistant Scale: intervals of values distributed in equal units-No true zero: doesn’t mean “absence” (such as 0 degrees F isn’t the absence of heat, just less)4. Ratio: refers to data on a scale with a true zero point-All properties of nominal, ordinal, and intervals scale (name + order + intervals + true 0)-Is an interval scale with a true zero (complete absence of data beingmeasured)Summation sign (∑ sigma)∑ = “the sum of”∑X = add all the scores for variable X∑x^2 = first square each value of X, then add all squared values∑(X+1) = first add 1 to each value of x, then add all x values)FREQUENCY DISTRIBUTIONS-Step one: Plot DataGraph or table, tells characteristics of data, patterns emerge-Frequency distribution: how often each observations occursBasic setup: X = score type (ex. how many males), categorical r numericalF = frequency of occurrenceCategorical frequency distribution table (used for nominal/ordinal data)-Contingency table: look at 2 categorical variables simultaneously Shows joint frequency of crossing two variablesMarginal Distribution: depicted in the “total” columns-Calculating Σ � from Frequency Table:1. Recreate the original set of scores and sum them up2. Multiply each score (X) with its frequency (f ) and then add up the resultingvalues (ex. 15(.25) + 30(.50) + 32(.25) = ____ )-Group Frequency Table (when you have too wide of a range of numbers, scores get grouped into class intervals)Suggestions: 1. There should be about 10 class intervals 2. The width of each interval should be a simple number (e.g. 2, 5, 10, or 20) 3. The bottom score in each class interval should be multiple of the width 4. All intervals should be the same width5. Equation for determining number of intervals and their width (always round up the number of intervals!)# of intervals = highest score-lowest score+1Interval widthRelative Frequency Distribution- p = f(X) / N - n or N = (number of observations, total frequencies)- p = percentage * 100Outliers-Extreme values in a frequency distribution; may be excluded, BUT make sure that you mention that the data has been excludedBar Graph-Type of histogram used to graph qualitative data-Each bar is separated from other barsHistogram***Different than bar graph b/c columns touch, histograms are continuous-Graph of a frequency distribution in which a rectangular bar is drawn over each value on the x-axis • Classes are plotted on the x axis – Interval or ratio scale, discrete • Frequency is plotted on the y axis – x axis: horizontal; y axis: verticalFrequency Polygon-line graph of frequency distribution, classes are plotted in the x axis ad frequencies plotted on y axis-Interval or ratio, continuous-line graph version of histogramShapes of Histograms and Frequency Polygons1. Normal Distributiona. Familiar bell shape curveb. Symmetricalc. Describes many naturally occurring phenomena2. Bimodal Distributiona. Two modes or “humps” (usually due to systematic influence)b. Most observations fall in or around one of two classesc. Ex). Ages of members of two generation families (parents and kids)3. Skewed Distributiona. With few extreme valuesb. Positively skewed: extreme values are largec. Negatively skewed: extreme values are smallCentral tendenciesMode: mostMean: sum of scores divided by numbersMedian: separates top 50% from bottom 50%-for odd numbers: Median position (N+1)/2-for even numbers: (n+1)/2, take average of scores