To run chi-square tests, all cells should have 1 or more than 1. No more than 20% of cells should have less than 5 cases per cell. In 3x4 table (12 cells), at most 2.4 cells (20% of 15) should have expected frequencies less than 5. In a 2x2 table, all cells must have 5 cases.

I have finished summarizing this book that meticulously explains descriptive and inferential statistics with a complete spss guide. The write-up examples are also useful.

Many students feel anxious about their mathematical expertise. However, understanding statistics will help them read and learn more about the research process and its role in various fields of interest (Alistair et al., 2009).

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Compared to the experimental design involving the laboratory settings, the quasi-experimental design allows researchers to use pre-existing groups or the same group for pre & post-tests. The non-experimental design is used to find connections between variables.

Data screening is to know the data and identify potential errors and problems with data before we proceed to analyses. The problems can be: - Missing values - Unusually large or small scores - Too few cases - Mistakes: incorrect or impossible score values

The scatterplot is the most important part of data screening for correlation. A <bivariate outlier> represents an unusual combination of X and Y. A bivariate outlier is an isolated data point outside the cloud. This can substantially inflate or deflate the r-value.

The term pooled means averaged. To obtain the pooled variances, we average the two within-group variances. In this case, the sample size (N) is the same: n1 = n2.

When equal variances are not assumed, separate the two variances instead of pooling them.

Post Hoc tests are protected tests because they limit the risk of Type I error. The Tukey HSD test is a moderately conservative post hoc. Even if F for one-way Anova is statistically significant, if between-group differences are not large enough, post hoc may not be significant.

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The normal distribution for percentile can be confusing. I found a figure that describes well the percentile. With this, we can calculate the area between two z scores. Ex) the area between 1.5 and -1 = 43.32% + 34.13% = 77.45%

The Nonparametric test, Mann-Whitney U always produces a two-tailed statistic, so we need to divide the p-value by two unless that is a two-tailed research hypothesis. For instance, the p = 0.12, will be p = .006 (Soleman, p. 208)

Dependent T-tests: 1. two repeated measures - the difference before & after treatment 2. two related topics - the different test scores between math and statistics 3. two conditions - the different depression levels after completing different therapies.

In Chi-square tests, the standardized residuals can be obtained by subtracting the expected from the observed frequencies and dividing it by the square root of its corresponding expected values. Over +1.96 or under -1.96 indicates a significant difference.

In the 2x2 contingency table, the phi coefficient can be adopted as the association level. Squaring the phi coefficient produces the variance in the dependent variable. For instance, squaring the -.33 phi means 10.89%, which indicates a weak relationship (Soleman, p. 308).

Why not use the independent t-tests to compare the means of categorical variables with more than 2 groups? Using multiple independent t-tests makes the type I error higher. The alpha must be adjusted to avoid making type I errors.

When is Ancova not appropriate? 1. if the variances of all groups on the DV are not equal. 2. if there is a significant interaction between the IDV and covariate variable. In this case, treat the COV as an IDV to conduct a multiple regression test (Soleman, pp. 249-250)

Beta (β) 's value is the same as R's in the regression tests. However, the beta can indicate the direction of the relationship between the IDV and DV, while the R does not show this.

For the research question, "Is there a difference in the fitness levels of men and women who fall into one of the different age groups?", you will need to conduct a Factorial Anova test, which examines the main effect of gender and age, including their interaction effect.