Research Methods Test 3 03 28 2012 PSY3213C Using Statistics to Answer Questions Chapter 9 Using Statistics to Answer Questions o Statistics Branch of mathematics that involves the collection analysis and interpretation of data o Two main branches of statistics assist your decisions in different ways o Descriptive Statistics o Procedures used to summarize a set of data o Measure of central tendency typical or representative score o Variability What spread exists in the scores o Inferential Statistics o Inferential statistics are used to analyze data after you have conducted an experiment to determine whether your independent variable had a significant effect Scales of Measurement Measurement The assignment of symbols to events according to a set of rules Scale of Measurement A set of measurement rules o Nominal Scale o Ordinal Scale Events are assigned to categories classify your research participants as men or women as right handed or left handed as Catholic or Protestant Differences between categories are qualitative kind and not quantitative degree Do number of individuals in one category differs as a function of some treatment Examples Jersey numbers telephones zip codes Permits events to be rank ordered usually single continuum that underlies a classification system Examples college football standings class standings might divide participants up on basis of creativity and end up with three categories noncreative creative highly creative If it can be ranked it is ordinal Degree of quantitative difference that nominal scale does not have Differences between consecutive values are not necessarily equal top 20 football teams difference between 1 and 4 not necessarily same as 6 and 9 don t know how much distance exists between ranks o Interval Scale Rank ordering and assumption of equal distance between ranks household thermometer ACT SAT often chosen because no true zero o Ratio Scale Rank ordering of events assumption of equal distance between ranks and a true zero point weight length calorie content of food Mode The score in a distribution that occurs most often can be more than one mode 12 15 20 20 20 Mode is 20 Median The number that divides a distribution into equal halves to calculate first rank them 56 15 12 20 17 12 15 17 20 56 Mdn 17 Mean The arithmetic average of a set of numbers It is found by adding all the scores in a set and then dividing by the number of scores Graphing results Pie Chart Graphical representation of the percentage allocated to each alternatives as a slice of a circular pie Histogram A graph in which the frequency for each category of a quantitative variable represented as a vertical column that touches the adjacent column o Levels of categories must be numerically ordered and arranged in order Bar graph A graph in which the frequency for each category of a qualitative variable is represented as a vertical column The columns of a bar graph do not touch o Can t be numerically ordered Example single married divorced and remarried Examining distribution Frequency polygon A graph that is constructed by placing a dot in the center of each bar of a histogram and then connecting the dots o Understand the shape of the distribution of scores especially helpful in comparing sets of data o Connected to the histogram made from histogram Line Graph a graph that is frequently used to depict the results of an experiment The vertical or y axis DV is plotted here is known as the ordinate and the horizontal or x axis IV is plotted here is known as the abscissa The location of the center of a distribution tells you where the scores tended to cluster along sale of measurement Note the spread of the scores o Do they tend to bunch up around the center or spread far from it The spread of scores indicates how variable they are Note the overall shape of the distribution o Is it hill shaped with a single peak at the center or does it have more than one peak If hill shape is more or less symmetrical or skewed Skewed distribution has a long tail trailing off in one direction and a short tail extending in the other direction o Positively skewed if long tail goes off to right or negative skewed it goes off to the left o Most variables in psychology tend to produce a normal distribution symmetric and hill shaped bell curve Look for gaps or outliers o Outliers are extreme scores that lie far from others well outside overall pattern of data o May be perfectly valid although unusual scores but sometimes they represent mistakes in data collection or transcription Measures of variability Variability the extent to which scores spread out around the mean largest score Range computed by subtracting the smallest score from the o Least informative measure of spread o Doesn t take into account the magnitude of the scores between the extremes and it is very sensitive to outliers o 1 2 3 4 5 6 range of 5 or 1 2 3 4 5 31 range of 30 Variance a single number that represents how much each scores varies from the mean the larger the number the greater the total spread of scores Standard deviation square root of the variance Inferential Statistics What is significant An inferential statistical test can tell us if the results of an experiment can occur frequently or rarely by chance o If something occurs often by change then its not significant and the IV is not responsible for affecting the DV o RULE OF THUMB Frequently by chance NOT significant 05 Rarely by chance Significant 05 What is the Null hypothesis It says that all differences between groups are due to chance i e not the operation of the IV o If result occurs rarely chance then we conclude that some factor other than chance is the reason and if we did our experiment correctly exercised control etc then we can assume that the IV we manipulated did affect the DV scores D 05 Results considered significant if it would occur 5 or fewer times by chance out of 100 repetitions of the experiment What is a T test review page 193 clothes study An inferential statistical test used to evaluate the difference between two means One IV with two levels o Customer clothing type IV 1st level Group A Dressy clothes 2nd level Group B Sloppy clothes The DV o How long it takes for the sales representative to approach the two types of customers n 16 clerks 8 randomly assigned to group A dressy 8 randomly assigned to group B sloppy They re independent groups each group will see a different situation from the other Higher scores reflect longer wait times for
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