Designing Effective Graphs

Abstract

Actuaries, like other business professionals, communicate quantitative ideas graphically. Because the process of reading, or decoding, graphs is more complex than reading text, graphs are vulnerable to abuse. To underscore this vulnerability, we give several examples of commonly encountered graphs that mislead and hide information. To help creators design more effective graphs and to help viewers recognize misleading graphs, this article summarizes guidelines for designing graphs that show important numerical information. When designing graphs, creators should:

• (1) Avoid chartjunk

• (2) Use small multiples to promote comparisons and assess change

• (3) Use complex graphs to portray complex patterns

• (4) Relate graph size to information content

• (5) Use graphical forms that promote comparisons

• (6) Integrate graphs and text

• (7) Demonstrate an important message

• (8) Know the audience.

Some of these guidelines for designing effective graphs, such as (6), (7) and (8), are drawn directly from principles for effective writing. Others, such as guidelines (3), (4) and (5), come from cognitive psychology, the science of perception. Guidelines (1) and (2) have roots both in effective writing and in graphical perception. For example, the writing principle of brevity demonstrates how eliminating pseudo three-dimensional perspectives and other forms of chartjunk improve graphs. As another example, the writing principle of parallel structure suggests using small multiple variations of a basic graphical form to visualize complex relationships across different groups and over time.

To underscore the scientific aspect of graphical perception, we examine the process of communicating with a graph, beginning with a sender’s interpretation of data and ending with a receiver’s interpretation of the graph. In keeping with scientific tradition, this article discusses several studies in the literature on the effectiveness of graphs.

We conclude that the actuarial profession has many opportunities to improve its practice, making communication more efficient and precise.     

Integration of Financial Services

Abstract

Integration financial services is a term with many meanings. Definitions might include:

• ownership of different segments of financial services,

• the distribution of products of one segment by another, and

• a consumer-centric strategy driven to satisfy the needs of the customer regardless of organizational structures.

For the purposes of my paper, I will define it as the erasing of boundaries leading to consumers receiving value propositions that are not restricted by traditional industry segment barriers.     

Holm's probability-paper tests in relation to the Kolmogorov—Smirnov one-sample test

Abstract

In [5] S. Holm proposed teststatistics for testing simple hypotheses by means of the probability paper for distribution functions (d.f.) of the form F ₀(x) = Φ[(x - μ₀)/σ₀], where μ₀ is location parameter, σ₀ scale parameter, and Φ is an absolutely continuous distribution function with Φ(0) = 1/2. If μ₀ and (σ₀ are known, the hypothesis H ₀ is:

• H ₀: H(x) = F ₀(x) = Φ[(x?μ₀)/σ₀],

while the three possible alternatives are

• H ₁: H(x) > F ₀(x)

• H ₂: H(x) < F ₀(x)

• H ₃: H(x) ≠ F ₀(x).

     

Sur la notion de prime d'épargne

Abstract

Il est bien connu que la réserve mathématique W (t) d'une assurance très générale sur la vie satisfait à une équation différentielle de Thiele, à savoir où l'on a

• δ (t) = le taux instantané ou l'intensité d'intérêt,

• μ (t) = l'intensité de mourir,

• P (t = la prime par unité du temps,

• S (t) = le capital assuré en cas de décès.

     

Accountancy and Academic/Professional Inter-dependency (or Mutual Exclusivity?)

This paper is a report on an Accounting Education Symposium held during the 2009 Annual Congress of the EAA in Tampere, Finland. This was the fourth occasion on which there has been an Accounting Education Symposium (or similar) within an EAA Annual Congress. Previous events were as follows:

• 2005 (Gotenburg, Sweden) EAA Accounting Educators' Forum

• 2006 (Dublin, Ireland) ‘Universities and Professional Bodies: Complementary or Colliding Roles in Educating and Training Future Accounting Practitioners?’ (sponsored by the Irish Accountancy Educational Trust)

• 2008 (Rotterdam, the Netherlands) ‘Accounting Education: The Common Content Project’ (sponsored by Royal NIVRA).

     

Economic policy and prospects

Though now into their second term of office, the Government are still trying to fulfil the objectives of the first ‐ to cut public spending and reduce taxes. The hard choices they eventually make will in part be dictated by the following sorts of considerations:

• technical ‐ year‐to‐year forecasts

• economic ‐ growth in gdp

• political ‐ reduction in income support.

At the centre of these and other often conflicting sets of considerations is the Chancellor of the Exchequer. Chancellors make many statements, but few are as clear as that made by Nigel Lawson, in the course of an interview with Max Wilkinson, economics editor of the Financial Times, from which we have extracted the following.     

Least squares,and a generalisation of the »Student»-Fisher theorem

Abstract

1. Following the methods employed by Steffensen ¹ a simple analytical proof of a generalisation of the »Student»-Fisher theorem is obtained. Geometrical proof of this generalisation has been given by Sterne.²     

On the central limit theorem

Abstract

If X and Y are mutually independent random variables whith the d. f. ¹ Distribution function(s) F ₁(χ) and F ₂(χ), it is known ² CRAMÉR (1), p. 35. that the sum X + Y has the d. f. F ₂(χ), defined as the convolution where the integrals are Lebesgue-Stiltjes integrals. One uses the abbreviation More generally the sum X ₁ + X ₂ + … + X _n of n mutually independent random variables with the d. f. ¹ Distribution function(s) F ₁(χ), F ₂(χ) , … , F _n has the d. f.      

The Bank Lending Channel Transmission of Monetary Policy in the EMU: A Case Study of Portugal

Abstract

This paper confirms the importance of bank performance to the credit-lending channel of monetary policy in the countries of the EMU and particularly in Portugal during recent years. The paper’s main innovations are (1) its use of macro and microeconomic statistical data; (2) the introduction of three calculated bank-performance indicators—asset structure, conversion of clients’ resources into credits and financial margins—into an adaptation of the Bernanke and Binder model; and (3) the use of panel data estimations not only to demonstrate the importance of the bank lending channel, but also to analyse the effects of the calculated indicators in bank-lending growth.     

Some remarks on the effect of selection upon mortality with regard to different causes of death

Abstract

In a previous number of this Journal ¹ Zum Studium der Sterblichkeit minderwertiger Leben. Skandinavisk Aktuarietidskrift 1921, p. 31. , I have given an account of an investigation into the increased mortality among certain groups of sub-standard risks based only on statistics of deaths. The material, collected for that investigation, can also be used as basis for an attempt of investigating the influence of Selection on the mortality among stan,dard risks.     

Early regulatory actions by the SEC: An institutional theory perspective on the dramaturgy of political exchanges

It has been urged that research be directed at understanding the development of political institutions, particularly administrative institutions, in the American governance structure, as well as their role in providing order and change in American politics. Toward this end, the purpose of this paper is to examine the development of one specific administrative institution, the Securities and Exchange Commission (SEC), and the effect of its regulatory actions in establishing the SEC's own legitimacy with Congress, the press and regulatees, particularly in terms of the McKesson and Robbins enforcement action. Our archival analysis, using primary and secondary material, probes the SEC's efforts at developing a dramaturgy of exchange relations with its external constituents in terms of its:

• 1. 

  (a) conformity to sanctioned language forms;

• 2. 

  (b) use of both the acquiescence and compromise strategies in dealing with external constituents and in balancing needs for the appearance of regulation with de facto inaction in regulating audit practice;

• 3. 

  (c) development and application of a ritualistic pattern of interacting with regulatees. We conclude that in order to understand the SEC as a political institution, it is necessary to incorporate an appreciation of its self-interested behavior in terms of the form, content and rhetoric of its regulatory actions. A critical facet of early SEC efforts and success did not concern whether it did good in terms of applying effective regulations, or bad in terms of preserving the status quo in power relations among the business and political communities. The ability of the SEC to legitimate its existence and institutionalize its role in the financial markets and in the financial reporting and auditing communities proved more essential.

     

Correlation once more

Abstract

§ 1. Correlation Generally.

In my thesis for Doctorship of 1919, ¹ This Journal, 1919, p. 1. I have made some critical remarks on the theory of correlation, trying especially to exhibit the rather unaccomplished state of this theory, and the danger of releasing its formulae for general use. In a supplementary note, ² Ibidem, p. 204. I have pushed my criticism a little further. Since that time, more than ten years have passed away, but I find my point of view still sustainable. One reproach, however, I have never been able to reject, viz, of having been exclusively negative. In fact, I find this position rather natural, from a philosophical standpoint. The information value of correlation calculations is indeed, as a rule, very small. And this seems the more regrettable, as the importance of the Στχαστι?? Τ?χυη, even for the most difficult questions of knowledge, ought to be very great. In a paper of 1924, “Quelques questions concernant les principes de la théorie des probabilités” ³ Ibidem, 1924, p. 107. I have tried to explain, how I imagine the development of the theory of correlation in order to be more apt to set about such philosophical questions.     

Note respecting the application of »The reduced number of deaths»

Abstract

This note is merely intended to supplement the remarks on the reduced number of deaths made by Olav Aabakken III his paper in this number of the journal ¹ Olav Aabakken: Appraisement of Under-average Lives in Norway, p. 126. .     

A. Palmström

Abstract

1. Mr R. Frisch has recently ¹ Ragnar Frisch: Sur les semi-invariants et moments employés dans l'étude des distributions statistiques, Oslo, 1926 (Det Norske VidenskabsAkademis Skrifter, II N:o 3), p. 26. established the interesting identity     

Functions of measurements under general laws of error

Abstract

The first object of this paper is to extend somewhat a theorem of MISES ¹ (1) Fundamentalsätze der Wahrscheinlichkeitsrechnung, (2) Grundlagen der Wahr. Mathematische Zeitschrift (1919) vol. 4, pp. 1–97; vol. 5, pp. 52–99. , who by the use of the STIELTJES integral ² Bliss, Integrals of Lebesgue, Bulletin of the American Mathematical Society, vol. 24 (1917), pp. 1–47. Bliss, A necessary and sufficient condition for the existence of a Stieltjes integral, Proceedings of the National Academy of Sciences vol 3 (1917), pp. 633–637. HILDEBRANDT, On Integrals related to and Extensions of the Lebesgue Integrals, Bulletin of the American Mathematical Society, vol. 24 (1917), pp. 113–144; Ibid., pp. 177–202. CARMICHEAL, Conditions necessary and sufficient for the existence of the STIELTJE'S Integral, Proceedings of the National Academy of Sciences, vol. 5 (1919), pp. 551–555. treats as a single subject continuous (geometric) and discontinuous (arithmetic) probability. Laplace ³ Oeuvres complete de LAPLACE, 3rd Ed., vol. 7, p. 266. , indeed, used a probability function which was in general continuous but had finite jumps, but he left no systematic treatment of the whole field of probability under such general conditions.     

Edvard Jäderin

Abstract

Im Jahre 1928 hat Frau Dr. H. Pollaczek-Geiringer ² H. Pollaczek-Geiringer: Die Charliersche Entwicklung willkür licher Funktionen, Skandinavisk Aktuarietidskrift 1928, p. 98–111. in dieser Zeitschrift einen Konvergenzbeweis für die Charlier'sche B-Reihe unter der folgenden Voraussetzung bewiesen:     

Withdrawal among Norwegian Life Assured 1910–1935

Introduction.

In the series of statistical experiences of the Norwegian life assurance companies report No. IV was issued some time ago. ¹ “Frivillig avgang blant norske livsforsikrede og dödeligheten blant forsikrede med fripolise 1910–1935”. Oslo 1943. The report, which was prepared at the Statistical Bureau of the Norwegian Life Assurance Companies, comprises 2 subjects: 1. Withdrawal among Norwegian life assured

2. Mortality among assured with paid-up policies (free policies) both during the period 1910–1935.

     

Measures of departure from symmetry

Abstract

1. Many different measures of skewness have been proposed. The textbook of Albert Waugh ¹ Elements of Statistical Method. New York and London 1938. for instance presents six different measures of skewness. Other measures of skewness have been proposed by Lindeberg ² Skandinavisk Aktuarietidsskrift. Vol. 7. (1925) p. 106. and Lenz ³ Erna Weber: Einführung in die Variations- nnd Erblichkeitsstatistik. München 1935. p. 92. . All these measures are zero when the distribution is symmetric, but any of them may be zero also when the distribution is unsymmetric. I shall here present some measures of skewness which are zero when and only when the distribution is symmetric.     

Optimum stratification of the logarithmic normal distribution: A comment

Abstract

In a recently published article Block has given the optimum points of stratification when the stratification variable and the estimation variable follow a two-dimensional logarithmic normal distribution. ¹ Eskil Block: “Numerical Considerations for the Stratification of Variables Following a Logarithmic Normal Distribution”, this Journal 1958, pp. 185–200.