Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35HP-340: Fall 2016 1 Health Behavior Statistical Methods HP 340L Lecture 3 Describing Data: Frequency Distributions and Graphs Chapter 3HP-340: Fall 2016 2  We covered:  Material in Kiess & Green Chapters 1-2  Key topics  Populations and samples  Parameters and statistics  Data and variables (independent and dependent)  Scientific Method (Hypotheses, experiments, observational research designs)  Discrete and continuous variables  Scales of measurement (nominal, ordinal, interval, ratio) Previous LecturesHP-340: Fall 2016 3  We will cover:  Material in K&G Chapter 3 – (Descriptive Statistics)  Key Topics  Graphs • Bar graphs & Pie graphs • Histograms & Frequency polygons  Frequency Distributions • Ungrouped and grouped scores • Cumulative distributions  Percentile Ranks and Percentiles Today’s LectureHP-340: Fall 2016 4  Pie charts and bar charts  Example from http://speakingppt.com Graphing Qualitative (nominal) VariablesHP-340: Fall 2016 5  Pie charts  Obtain frequencies and proportions of the total for each category of your variable  Draw a circle  Cut the circle into slices proportional to the proportions of each category  Not easy to do by hand!  Formally would need to divide 360 degrees of circle into appropriate angular sections Graphing Qualitative (nominal) VariablesHP-340: Fall 2016 6  Example: subject majors of students in HP-340 Graphing Qualitative (nominal) VariablesHP-340: Fall 2016 7  X axis: one bar for each group  Bars are separated on the X axis  Height of bar can be frequency or proportion Graphing Qualitative (nominal) VariablesHP-340: Fall 2016 8  Easier to assess relative frequencies in bar charts than in pie charts  Easier to assess relation to the whole from pie chart Pie vs. Bar ChartHP-340: Fall 2016 9  There is a chart building function in SPSS  Multiple types of charts can be created  Need to pay attention to the pie or bar options Pie and Bar Charts in SPSSHP-340: Fall 2016 10  Example: exam scores for 20 students 61 57 60 62 68 59 62 59 64 60 59 67 55 65 63 59 67 60 59 64  How do we make sense of these data?  What is the:  Most common score?  Lowest score?  Highest score? Graphing Quantitative (numerical) VariablesHP-340: Fall 2016 11  Histograms  Bar height indicates frequencies of class intervals Graphing Quantitative (numerical) Variables  Frequency polygons  Graph frequencies of class intervals at midpoints  Connect the midpointsHP-340: Fall 2016 12  Histogram rules  Frequency is shown by the height of the bar, size of each class shown by the width  No spaces between bars  Area of bar is proportional to frequency in the interval  Typically make all interval widths equal so the height is representative of frequency Graphing Quantitative (numerical) VariablesHP-340: Fall 2016 13  Example: Total cholesterol level (mg/dl) for a sample of 200 people  Note y-axis here is the relative frequency Graphing Quantitative (numerical) VariablesHP-340: Fall 2016 14  A distribution of scores, illustrated in a histogram, can take on a variety of shapes  We describe the distribution by:  Symmetry  Normality (“bell-shape”)  Skewness  Modality Shapes of Frequency DistributionsHP-340: Fall 2016 15  Symmetry  A symmetric frequency distribution, when folded in half at the midpoint, has identical halves  One side of the distribution is the mirror half of the other side. Shapes of Frequency DistributionsHP-340: Fall 2016 16  Normality  A Normal frequency distribution is symmetric and has a “bell shape” Shapes of Frequency DistributionsHP-340: Fall 2016 17  Skewness  A skewed distribution has scores clustered at one end of the distribution and occurring infrequently at the other end Shapes of Frequency DistributionsHP-340: Fall 2016 18  Negatively (left) skewed:  Left tail is pulled out  Long tail points toward negative or small values  Positively (right) skewed:  Right tail is pulled out  Long tail points toward positive or large values Shapes of Frequency DistributionsHP-340: Fall 2016 19  Example: Right skewed distribution  Example of left skewed distribution?  Grades on a really easy test Shapes of Frequency DistributionsHP-340: Fall 2016 20  Modality  Mode: the most frequently occurring score in a distribution  “Peak of the distribution” Shapes of Frequency DistributionsHP-340: Fall 2016 21  A unimodal distribution has only one mode (one peak)  A bimodal distribution has two modes (two peaks)  A multimodal distribution had >2 modes (>2 peaks) Shapes of Frequency DistributionsHP-340: Fall 2016 22  A table showing each possible score along with how frequently each score occurred  Frequency distributions may be  Ungrouped  Grouped  Frequency distributions are the building block for making histograms Frequency DistributionsHP-340: Fall 2016 23  Ungrouped frequency distribution  Raw data (also called raw scores):  Grades for 20 students who took a test Raw: 62, 64, 58, 61, 66, 64, 62, 59, 60, 60, 55, 58, 68, 61, 61, 57, 63, 63, 62, 62 Sorted: 68, 66, 64, 64, 63, 63, 62, 62, 62, 62, 61, 61, 61, 60, 60, 59, 58, 58, 57, 55 Frequency DistributionsHP-340: Fall 2016 24  What do we do with these data to construct an ungrouped frequency distribution?  List all possible score values from the lowest to highest scores observed  Place a tally mark beside a score each time it is observed  Calculate frequencies: number of observations for each score (numeric value of the tally)  N = total number of observations  Relative frequencies: rf = freq / N  Percentage frequencies: %f = rf ×100 Frequency DistributionsHP-340: Fall 2016 25 Frequency Distributions Score Tally Frequency Relative