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Understanding Your Results By David Kilgour 1 Statistics: What’s the point? • Observations researchers make are DATA • STATISTICS are a set of mathematical procedures for summarizing and interpreting data • To be a good methodologist you need a CONCEPTUAL skills 2 Statistics: What’s the point? • 2 types of stats: • Descriptive Statistics (“the easy ones”) • Summarize the data in numbers • Inferential Statistics Make inferences about the meaning of the data (infer that the results from the sample apply to the population) 3 Descriptive Statistics • Measures of Central Tendency (the typical response) • Mean: The sum of all scores divided by the total number of scores (M) • Median: The midpoint (Mdn) • Mode: The most frequent score 4 Descriptive Statistics Variability (the amount by which subjects vary from one another) • Variance and Standard Deviation: The “standard” amount by which all of the scores deviate from the mean • SD = √Σ (x – M)^2/N • (x = each score; M = mean; N = number of scores) 5 Descriptive Statistics in a Nutshell • Central tendency tells you about the “average” person • Variability tells you how much people differ from the “average” person • Great for organizing and summarizing data but they are only 1/2 the picture… 6 • How do you deicide if the group differences are reliable and not due to chance alone? 7 Inferential Statistics • It is not possible to study an entire population so we use a sample of the population • Inferences are made about the likelihood that differences in the sample reflect differences in the population • Inferential statistics tell us if differences in the sample are large enough to conclude that there are differences in the population (“moving from the sample to the population”) 8 Inferential Statistics • Inferential statistics establish a probability that the results are real (not due to error) • Data with a probability (alpha level) less than 5% (p = .05) are regarded as statistically significant • This means 5 times out of 100 the results are going to be due to random error 9 Points to Ponder • Statistical significance allows us to say that our results are probably not due to chance • ‘Significance’ only refers to statistical probability, not to the theoretical or practical importance 10 Choosing a Statistic My research Question is about … Differences Frequencies between means Relationships Between variables t test, ANOVA Chi-Square Correlation Coefficients Interval / Ratio Nominal Ordinal Interval/Ratio 11 Chi-Square Test • Nominal data → frequency count • Observations can only belong to one category (e.g., male OR female) • Total # of observations = total # of participants • χ2 = Σ(O – E)^2/ E • O= Observed frequencies (your data) • E = Expected frequencies (null hypothesis) 12 Qualitative Data • Code observations to identify the main categories/themes/trends/patterns in the data • The goal of qualitative research is to provide a description of the context • Specific examples (snapshots) help to clarify the patterns • Use subheadings in the Results to identify the main trends (method or pattern based) 13 Qualitative Data • Open-Ended Interviews The data from the open-ended interviews with students and teachers are consistent with the questionnaire data. Specifically, students commonly reported that teachers controlled and directed their work to a much lesser degree when students worked on-line than otherwise. As one high-school student put it: It’s really like she [the teacher] acts different, because when she is teaching the class, it’s sort of stuff we have to do – you know, assignments we have to do. But on the internet, we have a lot more freedom to do almost whatever we want as long as we’re getting the work done… 14 15