PSY 2400, Week 2 Notes
PSY 2400, Week 2 Notes Psy 2400
Popular in Statistical Methods
Popular in Psychology (PSYC)
This 18 page Class Notes was uploaded by Natalie on Saturday September 10, 2016. The Class Notes belongs to Psy 2400 at Texas Tech University taught by Amelia Littlefield in Fall 2016. Since its upload, it has received 10 views. For similar materials see Statistical Methods in Psychology (PSYC) at Texas Tech University.
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Date Created: 09/10/16
PSY 2400 – Statistical Methods 09/06/2016 ▯ Independent/Dependent Variables Independent variable (IV) is the variable manipulated by the researcher o Independent because no other variable in the study influences it value – it is randomly assigned Dependent variable (DV) is measured to assess the effect of manipulation/treatment o Dependent because its value is thought to depend on the value of the independent variable ▯ Experimental Method: It’s all about control Methods of control o Random assignment of subjects o Matching of subjects (e.g., based on age, race, sex) o Statistically adjusting for the influence of some potentially influential variables of interest (e.g., covariates) Experimental condition o Individuals receive the experimental treatment or manipulation of interest Control condition o Purpose: to provide a baseline for comparison with the experimental condition o Individuals do not receive the experimental treatment They either receive no treatment (“business as usual”) or they receive a neutral, placebo treatment ▯ Non-experimental Mehtods Non-equivalent groups o Researches compares two or more groups o Researcher cannot control who goes into which group o Does depend on people Pre-test/post-test o Individuals measured at two points in time o Researcher cannot control influence of the passage of time o Not independent on passage of time Independent variable is only really then quasi=independent Variables and Measurement Scores (actual values given by participants) are obtained by observing and measuring variables that scientists use to help define and explain behavior Scaffolding of research ▯ Cosntructs and Operational Definitions Constructs o Internal attributes or characteristics that cannot be directly observed o Don’t exist in real world o Useful for describing and explaining behavior and attitudes ideal form o Plato o Have to think about what “love” looks like and where we learn it from operational definitons o identifies how we plan to measure an observable behavior o resulting measurement is used as a definition and a measurement of a construct “CHAIRNESS” o to define functional chair outcome would be behavioral not aesthetic o regardless, however we’re operationalizing it, we’re the ones defining the construct “LOVE” o can’t be directly observed but useful for us to describe things o so many different ways to measure little things years together sexual intercourse o whatever way measuring it is how you define it ▯ Kinds of Variables Date o Qualitative Categorical A.K.A. nominal (to name/categorize) o Quantitative Numerical, can be ranked Discrete Countable in whole numbers Continuous Can be decimals ▯ Discrete vs Continuous Variables Discrete variable o Has separate, indivisible categories E.g., US States, # of tweets, # of cars on a lot o No values can exist between two neighboring categories Continuous variable o Have an infinite number of possible values between any two observed values o Every interval is divisible into an infinite number of equal parts ▯ Real Limits of Continuous Variables Apparent limits (implicit categorization that we know we are making_ ae in units of original scale of measurement (e.g., how much do you weigh?) Real Limits are the boundaries of each interval representing scores measured on continuous number line o He real limit separating two adjacent scores is exactly halfway between the two scores o Each score has two real limits: The upper real limit marks the top of the interval The lower real limit marks on the bottom of the interval ▯ Scales of Measurement We measure our DV ( outcome of interest ) How we measure it has relevance for the Statistical tests we can use to answer our research question o Four Types of Scales Nominal Label and categorize No quantitative distinctions Ex Gender Diagnosis Experimental or control Academic major Categorical (names) Ordinal Categorizes and organizes by rank, size, or magnitude in a meaningful way Ordinals can be ordered Ex Rank in class Clothing sizes (S,M,L) Olympic medals Nominal, plus can be RANKED in increasing or decreasing order Ratio Ordered categories Equal interval between categories Meaningful and precise zero point Ex. Umber of correct answers Time to complete task Gain in height since last year Interval, plus ratios are consistent, and there is a meaningful zero value Interval Ordered categories Intervals between categories are of equal size Arbitrary or absent zero point value Ex Temperature, IQ, golf scores (above/below par) Ordinal, plus intervals are consistently the same size Measurement assigns individuals or events to categories or values o The categories can simply be names such as male/female or employed/unemployed o They can be numerical values such as 68 inches or 175 pounds The complete set of possible values makes up a scale of measurement for a given variable Relationships between the categories determine different types of scales ▯ Statistical KNOW-tation Statistics uses operations and notation you have already learned o Appendix A has a Mathematical Review PEMDAS – Please Excuse My Dear Aunt Sally o Parantheses o Exponents o Multiply/divide o Add/subtract Statistics also uses some specific notation o Scores are referred to as X (and Y) o N is the number of scores in a population o N is the number of scores in a sample Summation KNOW-tation Any statistical procedures sum (add up) a set of scores The summation sign, Σ, stands for summation o Whatever symbol or equation follows the Σ defines what need to be summed o Summation is done AFTER operations in parentheses, exponentiation, squaring, and multiplication or division o Summation is done BEFORE other addition or subtraction PEMDSAS- Please Excuse My Dear Sassy Aunt Sally o Parentheses o Exponents o Multiply/divide o Summation o Add/subtract ▯ Practice Summation Notation (homework) Teacher Demonstration o Problems in Ch. 1: Questions 18, 20 On your own: o Problems in Ch.1 Questions 19, 21, 23 Appendix A o Math skills review on your own time ▯ PSY 2400 – Statistical Methods 09/08/2016 ▯ Chapter 2 – Frequency Distributions ▯ Learning Outcomes Understand how frequency distributions are used Organize data into a frequency distribution table And into a grouped frequency distribution table Know hot to interpret frequency distributions Organize data into frequency distribution graphs Know how to interpret and understand graphs ▯ Chapter Concepts Frequency tables Histograms Various shapes of frequency distributions ▯ Tools you will need Proportions (math review, appendix A) o Fractions o Decimals o Percentages Scales of Measurement (Chapter 1) o Distinguish between nominal, ordinal, interval, and ratio variables o Identify continuous and discrete variables Real limits (Chapter 1) ▯ Frequency Given a set of scores, how can we make sense of them? o Provide a frequency Number of scores with a particular value If 5 students reported that their level of happiness when taking a statistics exam was a 2 on a 0-10 scale, the frequency for a rating of 2 would be 5 o Need to convey more? Provide a frequency table A table displaying the pattern of frequencies over difference values of the variable Frequency Distributions A frequency distribution is o A way to organize information o Shows the number of individuals (f) in each category value on the scale of measurement Either a table or a graph Always includes o The categories/values that make up the scale o The frequency (f), or number of individuals, in each category ▯ Frequency Distribution Tables Structure of frequency distribution tables o Categories in one column (typically ordered from highest to lowest but could be reversed) o Frequency count next to category in another column Σf = n (i.e., sample size) of your sample To compute ΣX from a frequency table o Convert table back to original scores and some Or o Compute ΣfX ▯ Proportions and Percentages Proportions o Measures the fraction of the total group that is associated with each score o Proportion –= p = f / N o Called relative frequencies because they describe the frequency (f) in relation to the total number (N) Percentages o Expresses relative frequency out of 100 o Percentage = p(100) = f / N (100) o May be included as a separate column in a frequency distribution table ▯ How To: make a frequency table Step 1 o Make a list down the page of each possible value, from lowest to highest Step 2 o Go one by one through the scores, making a mark for each next to its value on the list Step 3 o Make a table showing how many times each value on your list was used Step 4 o Figure the percentages of scores for each value ▯ Grouped frequency distribution tables If the number of categories is very large they are combined (grouped) to make the table easier to digest NOTE o However information is lost when categories are grouped Individual score values cannot be retrieved The wider the grouping interval, the more information is lost ▯ “rules” for grouped frequency distributions requirements (mandatory) o l intervals must be the same width o make the bottom (low) value in each interval a multiple of the interval width rules of thumb (suggested) o ten or fewer class intervals is typical and easy to digest (but use goo judgment for the specific situation) o choose a “simple” number for interval width (e.g., intervals of two or five or ten) ▯ Rules for Intervals in Grouped Frequency Distributions There should be 5-20 interval (10 or fewer suggested by Dr. Talley) The interval smust be mutually exclusive o Next variable should start w/ no overlap b/w last variable The intervals must be continuous (i.e., not “jump over’ possible values) o Must note that there are zeros there The intervals must be exhaustive (include all scores in date) He intervals must be equal in width Construct a Grouped Frequency Distribution The following date represent the record high temperatures for each of the 50 states Construct a grouped frequency distribution for the data using SEVEN groups/intervals 112 100 127 120 134 118 105 110 109 112 110 118 117 116 118 122 114 114 105 109 107 112 114 115 118 117 118 122 106 110 116 108 110 121 113 120 119 111 104 111 120 113 120 117 105 110 118 112 114 114 Step 1 – determine the groups o Find the interval width by dividing the entire range of scores by the number of intervals you want (7 in this example) Range = high – low = 134 – 100 =34 width = range/7 = 34/7 = 5 rounding rule: always round up if there is a remainder o choose the lowest data value, 100, for the first lower interval limit o the subsequent lower interval limits are found by adding the width to the precious lower interval limits Interval Limits The first upper 100 -val 104it is one less than the next lower interval limit (mutually exclusive). The subsequent upper inte109l limits are found by adding the width to the previous upper interval limits (contiguous intervals). 105 - 114 110 - 115 - 119 120 - 124 125 - 129 130 - 134 he interval boundary is midway between an upper class limit and a subsequent lower class limit first interval has an upper limit 104.49 and a lower limit of 99.5 Step 2 – tally the data Step 3 – find the frequencies Discrete Variables in Frequency or Grouped Distributions Constructing either frequency distributions or grouped frequency distributions for discrete variables is not complicated o Individuals with the same recorded score had precisely the same measurements o The score is an exact, discrete score ▯ Continuous Variables in Frequency Distributions Constructing frequency distributions for continuous variables requires understanding that a score actually represents an interval o A given score actually could have been any value within the score’s real limits o Individuals with the same recorded score probably differed slightly in their actual performance (value was rounded off) Constructing group frequency distributions for continuous variables also requires understanding that a score actually represents an interval Consequently, grouping several continuous scores actually requires grouping several intervals Observed limits of the (grouped) intervals are always one unit saller than the real limist of the (grouped) interval. (why?) ▯ Frequency Distribution Graphs Pictures of the frequency tables o All have two axes o X-axis (abscissa) typically has categories/values of measurement scale increasing left to right o Y-axis (ordinate) typically has frequencies increasing bottom to top General principles o Both axes should have value 0 where they meet o Total height of the y-axis should be about 2/3 to ¾ of length of the x-axis ▯ Data Graphing Questions The answers to these questions determine which is the appropriate graph o What is your level of measurement? Nominal, ordinal, interval, or ratio? o Discrete or continuous data? o Are you describing samples or populations? ▯ Frequency Distribution Histogram Requires numeric scores (interval or ratio) Represent all scores on x-axis from minimum thru maximum observed data values Include all scores with frequency of zero Draw bars above each score (interval) o Height of bar corresponds to frequency of value in the date o Width of bar corresponds to score real limits ▯ How to Make a Histogram Step 1 o Make a frequency table or grouped frequency table Step 2 o Put the values at the bottom of the page Along the x-axis, from left to right, from lowest to highest For a grouped frequency table, the values are the midpoints of the interval (e.g., if the interval was from 2-3 the value would be 2.5 Step 3 o Make a scale of frequencies along the left edge of the page (0 will be at the bottom and the highest value will be at the top) Step 4 o Make a bar for each value ▯ Grouped Frequency Distribution Histogram Same requirements as for frequency distribution histogram EXCEPT o Draw bars above each (grouped) class interval Bar width is the class interval real limits Consequence? Apparent limits are extended out one- half score unit at each end of the interval ▯ Histograms Histograms use interval limits and frequencies of the classes ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ Frequency Distributions Show the pattern of frequencies over the various values (how the frequencies are spread out) o Unimodal distribution A histogram with one very high area o Bimodal distribution A distribution with two fairly equal high points o Multimodal distribution A distribution with two or more high points o Rectangular distribution When all values have approximately the same frequency ▯ Block Histogram A histogram can be made a “block” histogram Create a bar of the correct height by drawing a stack of blocks (one block per case) Block histograms show the frequency count in each bar ▯ Frequency Distribution Polygons List all numeric scores on the x-axis o Include all values even if the frequency is zero, f=0 Draw a dot above the center of each interval o Height of dot corresponds to frequency o Connect the dots with continuous lines o Close the polygon with lines to the y = 0 point Can also be used with grouped frequency distribution date Switching Gears Histograms and polygons are for numeric (ratio or interval) variables Bar graphs are for nominal and ordinal variables ▯ Graphs for nominal or ordinal data For non-numerical scores (nominal and ordinal data) use a bar graph o Looks kind of like a histogram o BUT s_p_a_c_e_s between adjacent bars indicates discrete categories Without a particular order (nominal) Non-measurable width of ranked categories (ordinal) ▯ Population Distribution Graphs For large populations, scores for each member are not possible to depict o Graphs based on relative frequencies (in samples0 o Graphs use smooth curves to indicate exact scores were not used Normal o Symmetric with greatest frequency in the middle o Common structure in data for many variables ▯ Frequency Distribution Shapes Researchers describe a distribution’s shape, in words, rather than drawing it Symmetrical distribution = each side is a mirror image of the other Skewed distribution: scores pile up on one side and taper off in a tail on the other o Tail on the right (highs cores) = positive skew o Tail on the left (low scores) = negative skew ▯ Practice Frequency Tables & Graphs Teacher demonstration o Problems in chapter 2: question 10, 16 Group Activity o Problems in chapter 1: questions 15, 19 ▯ ▯