KIN 4310 1st Edition Lecture 4Outline of Last Lecture I. ExampleII. Sample SelectionIII. Sample SelectionIV. Methods of SamplingV. Random SamplingVI. Systematic SamplingVII. Convenience SamplingVIII. Stratified SamplingIX. Cluster SamplingX. DefinitionsXI. DefinitionsXII. Definitions – Methodological DesignXIII. DefinitionsXIV. Strategies to Avoid ConfoundingOutline of Current Lecture I. Key ConceptII. DefinitionIII. Frequency DistributionsIV. Frequency Distributions continuedV. Making a Frequency TableVI. Frequency Distribution Ages of Best ActressesVII. Reasons for Constructing Frequency DistributionsVIII. Key ConceptIX. DefinitionsX. SkewnessThese 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.XI. HistogramXII. Interpreting HistogramsXIII. Frequency PolygonXIV. Dot PlotXV. Stemplot (Stem and Leaf)XVI. Pareto ChartXVII. Pie ChartXVIII. Scatter PlotXIX. Box PlotXX. Time Series GraphXXI. Other GraphsCurrent LectureI. Key Concepta. When working with large data sets, it is often helpful to organize and summarize data by constructing a table called a frequency distribution.i. Whole point is to help organize data so you can understand data and see things with just a glanceII. Definitiona. Frequency Distribution (or frequency table)i. Lists data values (either individually or by groups of intervals), along with their corresponding frequencies or countsii. It’s a table of numbers, not a graph or illustrationIII. Frequency Distributionsa. Express the frequency that each score occurs, usually in order from smallest to greatest scoreb. Tells how many examinees obtained each scorec. Tells the range of scores = highest score – lowest scored. Tells us the mode = most frequently occurring scoreIV. Frequency Distributions continueda. List data values (either individually or by groups of interval), along with their corresponding frequencies or countsb. The interval is called a class or finc. Helpful for summarizing large data setsd. Helpful for improving meaningfulnesse. Provides a basis for constructing graphsf. Break up data into bins (like a range of values like 10-19) g. How many values occurred in that class?V. Making a Frequency Tablea. Step 1: Order the scoresb. Step 2: Count how many of each scorei. In the example, the scores are bins that represent a numberc. Step 3: Calculate the cumulative frequencyi. In the example, it tells you the value 7 or less occurs 46 timesd. Step 4: Calculate the relative frequency (raw frequency divided by the total number of data points)i. In the example, 3/50 = 0.06ii. It represents proportionsVI. Frequency Distribution Ages of Best Actressesa. The data in the example is positively skewedb. Here, median is the best central tendency method to useVII. Reasons for Constructing Frequency Distributionsa. Large data sets can be summarizedb. We can gain some insight into the nature of datac. We have a basis for constructing important graphsVIII. Key Concepta. Histogram: a type of graph that portrays the nature of a data distributioni. An illustration of the frequency distributionii. A bar chart where the height of each represents frequencyIX. Definitionsa. Symmetrici. Distribution of data is symmetric if the left half of its histogram is roughly a mirror image of its right halfii. Lots of histograms are usually bell-shapedb. Skewedi. Distribution of data is skewed if it is not symmetric and if it extends more to one side than the otherX. Skewnessa. Symmetrici. Mode = mean = medianb. Skewed to the Left (negatively)i. Mean  median  modeii. Long tail points to the lefc. Skewed to the Right (positively)i. Mode  median  meanii. Long tail points to the rightXI. Histograma. A bar graph in which the horizontal scale represents the classes of data values and the vertical scale represents the frequenciesXII. Interpreting Histogramsa. One key characteristic of a normal distribution is that it has a “bell” shape. b. It’s fairly symmetrical, its rare to be perfectly symmetricalXIII. Frequency Polygona. Uses line segments connected to points directly above class midpoint valuesb. An illustration of frequency distribution but its not a histogram because it is not abar chartXIV. Dot Plota. A graph in which each data value is plotted as a point (or dot) along a scale of valuesb. Pre- computer daysXV. Stemplot (Stem and Leaf)a. Represents data by separating each value into two parts: the stem (such as the leftmost digit) and the leaf (such as the rightmost digit)i. Pre-computer daysii. Also shows histogram if you turn your headb. Bumpus’s Sparrowsi. Stem plots can get complicatedXVI. Pareto Charta. A bar graph for qualitative data, with the bars arranged in order according to frequenciesb. Qualitative datac. Not a histogram because the x-axis is not a numerical axis.d. Its always going to look like it is positively skewed but it is not, its just in frequency orderXVII. Pie Charta. A graph depicting qualitative data as slices of a pieb. Financial people with an agenda use this to really emphasize somethingXVIII. Scatter Plota. A plot of paired (x/y) data with a horizontal x-axis and a vertical y-axisb. Important with correlational studiesc. Can only construct if you have paired data so one subject has to have two measurements associated with itXIX. Box Plota. Boxes represent quartiles; Range shown by whiskers; extreme values shown as dotsb. Rule: whisker cant be longer than the box c. Each box itself has a midline (represents the medial) and the top of the box (3rd quartile) and the bottom of the box (1st quartile) d. The top whiskers represent the maximum valuee. The dots represent the outliersXX. Time Series Grapha. A graph of data that have been collected at different points in timeb. x-axis is time and it’s a line graphc. This shows trends over timeXXI. Other Graphsa. Don’t make a graph that doesn’t make senseb. Graphs are supposed to be quick and informative at a