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Residuals – distance from the predicted versus observed values |
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1 acceptable and 4 unacceptable distributions for data – clockwise from top… normal distribution(only acceptable one), left skewed (note the tail is on the left), platykurtotic(flat), leptokurtotic(pointy), right skewed (tail is on the right). In typical statistics, the researcher attempts to transform non-normal data so they are normally distributed. |
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Two-way ANOVA - Also called a 2 x 2 factorial design. Note that there are four combinations of factors… thus… male-Europe, female-Europe, male-Asia, female-Asia |
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Types of natural data distributions – just glad to have you hear that many types exist (normal, exponential, poisson, etc) |
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Data without equal variance – this is not good data for any statistical test |
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Data with relatively equal variance (contrast this with figure E, if you take your data and subject it to a data transformation such as arcsin, square –root, log transform, then this may make it (1) more normal and (2) have equal variance, which are two of the assumptions of T-tests and ANOVAs |
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3 Assumptions of T-tests & ANOVAs– Know all three... 1. Data are independent2. Residuals are normally distributed 3. groups have equal variance |
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Continuous & categorical data types – Know both exist. Also know that the
(1) type of data, (2) datas’ distribution, (3) your research questions are the three key bits of information that you use in choosing your statistical procedure |
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Sum of squares – used in the math of nearly every type of statistical procedure |
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Correlation – note… fit of data to line is designated by r-value |
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Regression – note… fit of data to line is designated by r2-value |
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Chi-square test – uses categorical predictors and responses |
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One-sample t-test - test is made between one observed group and one expected value (e.g., sample of crab shell measurements you made versus published crab shell value) |
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Independent t-test – test is made between two independent groups (e.g., does store brand or name brand cookies have more chips) |
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Paired t-test – test is made between two non-independent groups (e.g., two groups near each other in space or pre-post tests) |
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Repeated measures – It tests between groups or differences over time. Samples can be individuals or locations sampled over multiple time periods. |
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ANOVA – It tests among 3 or more groups |
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Post-tests – Significantly different groups are indicated by asteristics (as in this case) or by lower case letters (not shown) |
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Loglinear regression – uses both categorical predictor and response variables… is basically an n-dimensional chi-square test. |
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Logistic regression – uses response variable that is bimodally distributed humps (e.g., yes-no, alive-dead, present-absent) |
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MANOVA or Multiple Regression – uses may predictor variables and many continuous response variables… multivariate test |
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Ordination – multivariate method to find groups. Similarities are distances between points. |
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Cluster Analysis– multivariate method to find groups. Similarities are distances between nodes on a tree. |
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GLM – General Linear Model – All-purpose method to predict relationship between X and Y variables. Can be univariate (regression, correlation, T-test, ANOVA) or multivariate (logistic regression, multiple regression, MANOVA) |
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Matrix Algebra – math behind the scenes in most statistics |
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Kruskal Wallis Test – nonparametric version of the ANOVA, uses rank data to see if significant difference among groups |
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| Non-congruous patterns in bar charts |
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