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- https://stats.libretexts.org/Workbench/Learning_Statistics_with_SPSS_-_A_Tutorial_for_Psychology_Students_and_Other_Beginners/12%3A_Linear_Regression/12.03%3A_Multiple_Linear_RegressionIn this model, we now have three coefficients that need to be estimated: b 0 is the intercept, b 1 is the coefficient associated with my sleep, and b 2 is the coefficient associated with my son’s slee...In this model, we now have three coefficients that need to be estimated: b 0 is the intercept, b 1 is the coefficient associated with my sleep, and b 2 is the coefficient associated with my son’s sleep. However, although the number of coefficients that need to be estimated has changed, the basic idea of how the estimation works is unchanged: our estimated coefficients \(\ \hat{b_0}\), \(\ \hat{b_1}\) and \(\ \hat{b_2}\) are those that minimise the sum squared residuals.
- https://stats.libretexts.org/Workbench/Learning_Statistics_with_SPSS_-_A_Tutorial_for_Psychology_Students_and_Other_Beginners/09%3A_Categorical_Data_Analysis/9.07%3A_The_Fisher_Exact_TestThe Fisher exact test works somewhat differently to the chi-square test (or in fact any of the other hypothesis tests that I talk about in this book) insofar as it doesn’t have a test statistic; it ca...The Fisher exact test works somewhat differently to the chi-square test (or in fact any of the other hypothesis tests that I talk about in this book) insofar as it doesn’t have a test statistic; it calculates the p-value “directly”. I’ll explain the basics of how the test works for a 2×2 contingency table, though the test works fine for larger tables.
- https://stats.libretexts.org/Workbench/Learning_Statistics_with_SPSS_-_A_Tutorial_for_Psychology_Students_and_Other_Beginners/10%3A_Comparing_Two_Means/10.07%3A_Effect_SizeTo the extent that you care about the practical consequences of your research, you often want to measure the effect size relative to the original variables, not the difference scores (e.g., the 1% imp...To the extent that you care about the practical consequences of your research, you often want to measure the effect size relative to the original variables, not the difference scores (e.g., the 1% improvement in Dr Chico’s class is pretty small when measured against the amount of between-student variation in grades), in which case you use the same versions of Cohen’s d that you would use for a Student or Welch test.
- https://stats.libretexts.org/Workbench/Learning_Statistics_with_SPSS_-_A_Tutorial_for_Psychology_Students_and_Other_Beginners/09%3A_Categorical_Data_Analysis/9.08%3A_The_McNemar_TestThus, the null hypothesis in McNemar’s test is that we have “marginal homogeneity”. That is, the row totals and column totals have the same distribution: P a +P b =P a +P c , and similarly that P c +P...Thus, the null hypothesis in McNemar’s test is that we have “marginal homogeneity”. That is, the row totals and column totals have the same distribution: P a +P b =P a +P c , and similarly that P c +P d =P b +P d . Notice that this means that the null hypothesis actually simplifies to P b =P c . In other words, as far as the McNemar test is concerned, it’s only the off-diagonal entries in this table (i.e., b and c) that matter!
- https://stats.libretexts.org/Workbench/Learning_Statistics_with_SPSS_-_A_Tutorial_for_Psychology_Students_and_Other_Beginners/12%3A_Linear_Regression/12.07%3A_Regarding_Regression_CoefficientsThe units of measurement have a big influence on the regression coefficients: the b coefficients only make sense when interpreted in light of the units, both of the predictor variables and the outcome...The units of measurement have a big influence on the regression coefficients: the b coefficients only make sense when interpreted in light of the units, both of the predictor variables and the outcome variable. The basic idea is quite simple: the standardised coefficients are the coefficients that you would have obtained if you’d converted all the variables to z-scores before running the regression.
- https://stats.libretexts.org/Workbench/Learning_Statistics_with_SPSS_-_A_Tutorial_for_Psychology_Students_and_Other_Beginners/00%3A_Front_Matter/02%3A_InfoPageThe LibreTexts libraries are Powered by NICE CXOne and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the Californi...The LibreTexts libraries are Powered by NICE CXOne and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
- https://stats.libretexts.org/Workbench/Learning_Statistics_with_SPSS_-_A_Tutorial_for_Psychology_Students_and_Other_Beginners/10%3A_Comparing_Two_Means/10.02%3A_The_One-sample_t-testThe second block gives the results of the t-test showing the t-score (2.255), degrees of freedom (19), One-sided p-value (.018), Two-sided p-value (.036), the mean difference between our scores and th...The second block gives the results of the t-test showing the t-score (2.255), degrees of freedom (19), One-sided p-value (.018), Two-sided p-value (.036), the mean difference between our scores and the hypothesized value, and finally, the 95% confidence interval. Well, since the t-test is basically a z-test with the assumption of known standard deviation removed, you shouldn’t be surprised to see that it makes the same assumptions as the z-test, minus the one about the known standard deviation.
- https://stats.libretexts.org/Workbench/Learning_Statistics_with_SPSS_-_A_Tutorial_for_Psychology_Students_and_Other_Beginners/15%3A_EpilogueThere are no “do it yourself exercises”. And in general, I feel that there a lot of things that are wrong with the presentation, organisation and content of this book. I haven’t finished writing the s...There are no “do it yourself exercises”. And in general, I feel that there a lot of things that are wrong with the presentation, organisation and content of this book. I haven’t finished writing the substantive content yet, so it doesn’t make sense to try to bring it all together. But this version of the book is going to go online for students to use, and you will be able to purchase a hard copy too, so I want to give it at least a veneer of closure.
- https://stats.libretexts.org/Workbench/Learning_Statistics_with_SPSS_-_A_Tutorial_for_Psychology_Students_and_Other_Beginners/12%3A_Linear_RegressionThe goal in this chapter is to introduce linear regression, the standard tool that statisticians rely on when analysing the relationship between interval scale predictors and interval scale outcomes. ...The goal in this chapter is to introduce linear regression, the standard tool that statisticians rely on when analysing the relationship between interval scale predictors and interval scale outcomes. Stripped to its bare essentials, linear regression models are basically a slightly fancier version of the Pearson correlation (Section 5.7) though as we’ll see, regression models are much more powerful tools.
- https://stats.libretexts.org/Workbench/Learning_Statistics_with_SPSS_-_A_Tutorial_for_Psychology_Students_and_Other_Beginners/14%3A_Bayesian_Statistics/14.03%3A_Why_Be_a_BayesianAny time that you aren’t exactly sure about what the truth is, you should use the language of probability theory to say things like “there is an 80% chance that Theory A is true, but a 20% chance that...Any time that you aren’t exactly sure about what the truth is, you should use the language of probability theory to say things like “there is an 80% chance that Theory A is true, but a 20% chance that Theory B is true instead”. To me, this is the big promise of the Bayesian approach: you do the analysis you really want to do, and express what you really believe the data are telling you.
- https://stats.libretexts.org/Workbench/Learning_Statistics_with_SPSS_-_A_Tutorial_for_Psychology_Students_and_Other_Beginners/14%3A_Bayesian_Statistics/14.10%3A_SummaryThe help documentation to the contingencyTableBF() gives this explanation: “the argument priorConcentration indexes the expected deviation from the null hypothesis under the alternative, and correspon...The help documentation to the contingencyTableBF() gives this explanation: “the argument priorConcentration indexes the expected deviation from the null hypothesis under the alternative, and corresponds to Gunel and Dickey’s (1974) a parameter.” As I write this I’m about halfway through the Gunel and Dickey paper, and I agree that setting a=1 is a pretty sensible default choice, since it corresponds to an assumption that you have very little a priori knowledge about the contingency table.
