PSY 302: Chapter 2 Textbook Notes
PSY 302: Chapter 2 Textbook Notes PSY 302
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Date Created: 09/30/15
CHAPTER 2 Intro To Frequency Distributions Like we saw in chapter 1 the purpose of descriptive statistics is to simplify and organize data One of the most common procedures for doing this is with Frequency Distribution FD an organized tabulation from lowest to highest of the number of individuals located in each category on the scale of measurement and groups together scores that are the same This lets the researcher easily see all scores of a study at a glance Can be in table or graph form Frequency Distribution iabes o The simplest table lists different measurement categories X in a column from highest to lowest Beside every X value the frequency or the number of times that value happens is included EX A teacher wants to see the FD of his students39 scores on a quiz graded from 110 With the FD he can easily see if more students scored more 95 and 105 compared to ls and 25 o Obtaining ZX from a Frequency Distribution Table 0 Reminder Make sure when you39re trying to get FD from a table you multiply the values by how many times they occur before you add them together This is commonly represented as fo Where ffrequency Proportions ano Percentages 0 Proportion measures the fraction of the total group associated with each score If two people scored 4 on a test out of ten people then their fraction would be 210 0 Proportion p fN Often called relative frequencies because they describe frequency in relation to the total number 0 Percentages are also often used So if the proportion from earlier was 210 that means 210100 20 20 of the scores were a 4 Grouped Frequency Distribution 7abes GFD 0 Range The lowest and highest scores that occurred ie the range on a test was 41 the lowest96 the highest 0 4196 is a very large range and would make a very large FD table if we listed out all those scores Instead groupings occur ie people who scored in the 905 become one group as opposed to people who scored 91 92 93 and so on 0 These group intervals are called class intervals 0 Guidelines to a GFD Table Not required in studies but helpful 0 There should be about ten class intervals Not too many but not too few groups a The interval width should be a simple number ie 2 5 10 or 20 It makes it easy to see how the range is divided 0 The bottom score of the interval should be a multiple of the width ie if you39re counting by twos your lowest score should be two o All intervals should be the same width Real Limits from CH 1 and Frequency Distributions 0 Remember a continuous variable has an in nite number of intervals between two categories However with real limits any values that fall between said real limits end up being the real limit ie 79 83 and 82 both end up being 8 So when X8 occurs on a frequency distribution table three times it doesn39t actually mean you have X8 three times exactly Apparent Limits The lowest and highest score of a class interval ie 4049 With continuous variables however you39re actually measuring 395495 those are the real limits the next higher class interval would be 5059 but again you39re actually measuring 495595 This means 495 meets in the middle so there39s no gaps in the scale Frequency Distribution Graphs O O The Xaxis is also called the abscissa and the Yaxis is also called the ordinate Graphs can be misleading If you look at a set of data with numbers 41 43 47 49 increasing over time but label the Yaxis from 4050 it39s going to look like the numbers have spiked rapidly If you start labeling the Yaxis from 0 however you39d see little to no change concealing the data There needs to be a balance between the two to make the graph as accurate as possible Graphs For Ratio 0r Interval Data 0 There are multiple kinds of graphs depending on the type of data 0 Histogram Numerical scores are listed along the Xaxis Then a bar is drawn above each axis so the height of the bar corresponds to the frequency of the category For continuous variables the width of the bar extends to the real limits of the category For discrete variables the width extends half the distance to the adjacent category on each side In both cases each bar in a histogram touches Histograms can also be drawn with stacked blocks Each block represents one individual so the more blocks a numerical score has the higher the frequency Polygon Numerical scores are listed along the Xaxis A dot is then placed above each value to correspond with its frequency with a continuous line going through each dot and ending at 0 frequency on the Xaxis If you are graphing class intervals with a polygon you place the dot directly in the center of the lowest and highest limits in the interval Graphs for Nominal or Ordina Data 0 The frequency distribution is displayed with a bar graph which is essentially the same as a histogram except there39s space in between the bars emphasizing separate distinct categories 0 When determining what graph to use make sure you know what type of data you have Graphs For Population Distributions 0 Due to the large nature of populations there are two special features to help make bar graphs polygons and histograms for them 0 Relative Frequencies You usually can39t nd the absolute frequency in a population but you can nd this For example after shing in a lake for a while you nd out there39s twice as many salmon as there are tuna This can be represented in a bar graph where the salmon39s bar is twice as high as the tuna39s Smooth Curves It is customary to draw smooth lines instead ofjagged ones like in polygons for populations It shows you aren39t connecting dots real frequencies but are instead representing relative frequencies Normal Curve Normal is a speci c shape that can be precisely de ned by an equation So a normal curve is a symmetrical curve on a graph with the greatest frequency occurring in the middle The Shape of a Frequency Distribution 0 Sometimes researchers will describe a distribution by listing its characteristics as opposed to drawing a frequency distribution graph They39re described with quotshape central tendency and variabilityquot 0 Central Tendency Where the center of the distribution is located Variability Tells whether the scores are spread over a wide range or are clustered closely together 0 Nearly all distributions can be classi ed as symmetrical or skewed Symmetrical a vertical line can be drawn in the center to split it in half evenly Skewed An asymmetrical curve If the curve piles up at the left of the scale it39s a positive skew with the tail pointing to the right If it piles up at the right of the scale it39s a negative skew with the tail pointing to the left Tail Of The Distribution Where the scores taper off
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