Up to now, we have dealt with various foundational aspects of random variables and their distributions. We have occasionally touched on how these variates can arise in practice. In the second part of this book, we start analyzing in more detail how the variates are connected with sampling situations, how we can estimate the parameters of their distributions (which are typically unknown in practice), and how to conduct inference regarding these estimates and their magnitudes. This chapter starts with the first of these three aims. We study the sample mean and variance and their sampling properties, but also the sample's order statistics and extremes. The empirical distribution function (EDF) is defined and analyzed. In the case of multivariate normality, the Wishart distribution arises as a generalization of the chi-squared. We study the properties of matrix Wishart variates. We also show how Hotelling's T² arises as the counterpart of Student's t in the case of multivariate samples. The density of the correlation coefficient is also derived. We introduce rank and sign correlations, known as Spearman's rho and Kendall's tau, respectively.

After World War II, the United States and the Soviet Union became the leading nations of the world. The two superpowers stood in uncompromising opposition to each other as leaders of two separate political blocs, but with the exception of the Korean and Vietnam Wars, the Cold War did not lead to armed conflict.

Social development in the United States was stable for a time, accompanied by prodigious growth in technology, science, and the economy. Tensions increased at the beginning of the 1960s, however. The United States deepened its involvement in the war in Vietnam, and differing viewpoints on this war effort came to divide the nation in two. The assassination of President John F. Kennedy in 1963 came as a shock, while the Civil Rights movement acquired a large following. The women's movement and, towards the end of the decade, the environmental movement gained momentum as well. Many young Americans turned against what they considered a materialistic and self-satisfied society and sought a more spontaneous and less conventional lifestyle.

As we have seen in the preceding chapters, psychology in the United States was undergoing rapid development during the time between World War I and World War II. After the Nazis seized power and Germany then lost World War II, psychology stagnated in both Germany and Austria. In the first half of the 1900s, the British took little interest in psychology, but in the 1950s, British psychologists again began to make contributions to the study, as did Canadian. Still, in the latter half of the twentieth century, empirical psychology was dominated by the United States, and in this chapter, I shall for the most part discuss the history of psychology in the United States.

Expansion in US Psychology

Psychology had proved to be important in preparing for and waging war. This increased interest in it, and psychological research enjoyed substantial funding from the US government after the war. The opportunity to study at universities was also considerably broadened when the government gave war veterans the right to three years of higher education. Students flocked to the field of psychology.

The first and the most important consequence of the principles established above is that only the general will can direct the forces of the State according to the end of its institution, which is the common good: for while the opposition of particular interests made the establishment of societies necessary, it is the agreement of these same interests that made it possible. What these different interests have in common is what forms the social bond, and if there were not some point on which all interests agree, no society could exist. Now, it is solely in terms of this common interest that society should be governed.