QUANTITATIVE RESEARCH AND BASIC STATISTICS

TODAYS AGENDA Progress, challenges and support needed Response to TAP Check-in, Warm-up responses and TAP Quantitative Data Analysis Interactive LectureTeam AssignmentFor next week

RESULTS OF TAP Concerns Assignment due on Halloween Increased feedback and access to instructor Class in-person for AHRD students Response Now due on November 3 rd at 11:59pm Alex will hold a Research Methods lab Here we are More feedback Adjustment to graduate school Back-to-back assignments Readings further in advance

ACTIVITY – AN UNUSUAL EPISODE Look at the following data sets. What do you notice about the numbers? What episode is this data depicting?

AN UNUSUAL EPISODE

AN UNUSUAL EPISODE: WHAT DO YOU NOTICE? Wealthy

WHAT IS THE “UNUSUAL INCIDENT”?

STATISTICS Allow researchers to describe information from many different scores with just a few numbers, ex. mean, median, mode When calculated for a sample derived from a population you get statistics. When calculated for an entire population, they are parameters.

WHY STATISTICS? Statistics help us analyze what is happening around us as well as help predict trends and make inferences.

QUANTITATIVE AND CATEGORICAL DATA Quantitative – data obtained when the variable being studied is measured along a scale that indicates the amount of the variable present. Reported in scores. Categorical – data that indicates the total number of objects, individuals or events a researcher finds in a particular category.

TYPES OF DATA Ratio – interval data with a natural 0, ex. Kelvin scale Interval – quantities that have an order where the intervals are equal ex. temperature Nominal – categorical ex. Car name Ordinal – quantities that have an order, team rankings, class ranking. Intervals between ranking is not necessarily equal

MEASURES OF CENTRAL TENDENCY Mean – average of all the scores in a distribution. Add up all scores and divide by total number. Mode – most frequent score in a distribution, does not tell us much about the distribution. Median – the point below and above which 50% of the scores fall, middle point. In a normal distribution the mean, median and mode are the same

THE NORMAL DISTRIBUTION Bell shaped curve Plots the mean, median and mode

WAYS TO SUMMARIZE QUANTITATIVE DATA Frequency distributions Histograms Stem and leaf plots Box plots

FREQUENCY DISTRIBUTION A way of putting statistical data in order Helps to make sense of the data gathered Lists scores from high to low Frequency polygon is a visual representation of this data Raw ScoreFrequency n = 50

FREQUENCY POLYGON Can be negatively or positively skewed Positive Negative

HISTOGRAM Is a bar graph used to display quantitative data at the interval or ratio level Frequencies are displayed on the vertical axis, scores on the horizontal

STEM AND LEAF PLOT This is used to display data in a way that shows both its shape and distribution Similar to a histogram, but instead of bars it shows values for each category

FIVE NUMBER SUMMARY AND BOX PLOTS Consists of the lowest score, the 25 th percentile (Q1) the 50 th percentile, the 75 th percentile (Q3) and the highest score

VARIABILITY When distributions have the same mean and median but differ in spread

STANDARD DEVIATION Most useful index of variability It is a single number that represents the spread of a distribution The smaller the standard deviation, the more closely spaced the scores are (less variable) The greater the standard deviation, the more spread out the scores are (more variable)

THE STANDARD DEVIATION OF A NORMAL DISTRIBUTION Total area under curve represents all the scores 50% of scores fall on either side of the mean

BREAK AND ACTIVITY

INTERPRETING QUANTITATIVE RESEARCH AND STATISTICS Being able to read and critique research is a necessary skill Need to know what is sound research and what is not Want to be a critical consumer of quantitative research

COMMON TERMS Z score – Simplest form of standard scores how far a raw score is from the mean in standard deviation units. Useful because allows for comparison of raw scores on different tests. T scores – raw scores that are bellow the mean of a distribution. The same as negative z scores.

COMMON TERMS Correlation – expresses the relationship between two variables Pearson Product Moment Coefficient- frequently used, know as Pearson r. Ranges between -1 and +1 Eta – similar to Pearson r but ranges from.00 to 1.00

COMMON TERMS Standard Error of the Mean – standard deviation of of a sampling distribution of means. Confidence intervals – boundaries indicated by the SEM If a confidence interval is 95%, there would be a “ probability ” that 5 out of 100 (population mean) would fall outside the boundaries or limits.

HYPOTHESIS TESTING The Research Hypothesis – specifies the predicted outcome of a study or the nature of the relationship that exists. The Null Hypothesis – specifies that there is no relationship. “There is no different between the population mean A and the population mean B”

DIRECTIONAL VS. NON-DIRECTIONAL HYPOTHESES Directional – indicates the specific direction (higher, lower, more) that a researcher expects to emerge in a relationship. Non-directional – does not make a specific predication about what direction the outcome of the study will take.

SIGNIFICANCE Statistical Significance – means that the results are likely to occur by chance less than a certain percentage of the time. Does not necessarily mean anything, large enough random sample will lead to significance no matter what Significance level - the probability of a sample statistic occurring as a result of sampling error (.05 and.01 are most common P value – helps determine significance of results, small P.05/.01 means there is little evidence against the null.

ONE AND TWO TAILED TESTS One tailed test – uses only the positive tail of a sampling distribution, is used when a researcher makes a directional hypothesis. Two tailed test – uses both sides of a sampling distribution, is used when a researcher makes a non- directional hypothesis.

ONE AND TWO TAILED TESTS

ANALYSIS OF VARIANCE (ANOVA) Used by researchers to see if there is a a significant difference between the means of more than two groups. Variation within the the groups and between the groups is statistically analyzed, this generates an F value. F value is checked against a table to see if it is statistically significant

T-TEST FOR MEANS Used to see if the difference between the means of two samples is significant t – Test for independent means – used to compare the mean scores of two different groups t – Test for correlated means – used to compare the mean scores of the same group before and after a treatment

ANALYSIS OF COVARIANCE (ANCOVA) A variation of an ANOVA Used when a researcher administers a pre-test related to the dependent variable, can adjust the post-test mean scores so to compensate for initial differences.

MULTIVARIATE ANALYSIS OF VARIANCE (MANOVA) Differs from an ANOVA by incorporating two dependent variables in the same analysis. Used only when a researcher believes there are correlations between the dependent variables

CHI – SQUARE Test used to analyze categorical data Based on a comparison between expected frequencies and actual obtained frequencies. If obtained frequencies are similar to expected than the two groups do not differ If obtained frequencies are different then there is a significant difference between groups

POWER OF A STATISTICAL TEST Power is the probability that the test will lead to the conclusion that there is a difference when a difference does in fact exist.

SO WHAT DOES IT ALL MEAN? Initially it’s going to be a little difficult to know what to look for. Results are important. Although the discussion talks about them, it’s important to read and interpret them yourself.

SO WHAT’S IT MEAN? CONT.

WHAT’S IT MEAN? CONT.