Long Tail

Examples of Long Tail in the following topics:

• Histograms and shape

  • Data sets with the reverse characteristic - a long, thin tail to the left - are said to beleft skewed.
  • We also say that such a distribution has a long left tail.
  • When data trail o in one direction, the distribution has a long tail.
  • If a distribution has a long left tail, it is left skewed.
  • If a distribution has a long right tail, it is right skewed.

• Shapes of Sampling Distributions

  • The shape of a distribution is sometimes characterized by the behaviors of the tails (as in a long or short tail).
  • For example, a flat distribution can be said either to have no tails or to have short tails.
  • A normal distribution is usually regarded as having short tails, while a Pareto distribution has long tails.

• Double-Stranded DNA Bacteriophages

  • The tail section of the virus punches a hole through the bacterial cell wall and plasma membrane and the genome passes down the tail into the cell.
  • After the head maturation, the tail is joined in one of two ways: either the tail is constructed separately and joined with the connector, or the tail is constructed directly onto the phage head.
  • The tails consist of helix-based proteins with 6-fold symmetry.
  • The Myoviridae have long tails that are contractile, the Podoviridae have short noncontractile tails, and the Siphoviridae have long non-contractile tails.
  • Siphoviridae constitute the majority of the known tailed viruses .

• Virulent Bacteriophages and T4

  • Many viruses can exist inside a host for long periods during which little damage is done.
  • Its double-stranded DNA genome is about 169 kbp long and is held in an icosahedral head, also known as a capsid.
  • Its tail fibres allow attachment to a host cell, and the T4's tail is hollow so that it can pass its nucleic acid to the cell it is infecting during attachment.
  • The T4 Phage initiates an E. coli infection by recognizing cell surface receptors of the host with its long tail fibers (LTF).
  • The baseplate changes conformation and the tail sheath contracts causing GP5 at the end of the tail tube to puncture the outer membrane of the cell.

• Sexual Selection

  • Males are often larger, for example, and display many elaborate colors and adornments, such as the peacock's tail, while females tend to be smaller and duller in decoration.
  • For example, while the male peacock's tail is beautiful and the male with the largest, most colorful tail will more probably win the female, it is not a practical appendage.
  • There is some evidence that this risk, in fact, is why females like the big tails in the first place.
  • Because large tails carry risk, only the best males survive that risk and therefore the bigger the tail, the more fit the male.
  • This male bird of paradise carries an extremely long tail as the result of sexual selection.The tail is flamboyant and detrimental to the bird's own survival, but it increases his reproductive success.This may be an example of the handicap principle.

• Factors Affecting Power

  • Power is higher with a one-tailed test than with a two-tailed test as long as the hypothesized direction is correct.
  • A one-tailed test at the 0.05 level has the same power as a two-tailed test at the 0.10 level.
  • A one-tailed test, in effect, raises the significance level.
  • The relationship between μ and power for H0: μ = 75, one-tailed α = 0.05, for σ's of 10 and 15.
  • The relationship between significance level and power with one-tailed tests: μ = 75, real μ = 80, and σ = 10

• Chordates and the Evolution of Vertebrates

  • Adults only maintain pharyngeal slits and lack a notochord, a dorsal hollow nerve cord, and a post-anal tail.
  • Members of Cephalochordata possess a notochord, dorsal hollow nerve cord, pharyngeal slits, and a post-anal tail in the adult stage.
  • Lancelets are only a few centimeters long and are usually found buried in sand at the bottom of warm temperate and tropical seas.
  • (c) In the adult stage, the notochord, nerve cord, and tail disappear.
  • Adult lancelets retain the four key features of chordates: a notochord, a dorsal hollow nerve cord, pharyngeal slits, and a post-anal tail.

• Mutually Exclusive Events

  • Let A = the event of getting at most one tail. ( At most one tail means 0 or 1 tail. ) Then A can be written as { HH, HT, TH } .
  • The outcome HH shows 0 tails.
  • HT and TH each show 1 tail.
  • Of the female students, 75% have long hair.
  • Let L be the event that the student has long hair.

• One- and Two-Tailed Tests

  • A probability calculated in only one tail of the distribution is called a "one-tailed probability. "
  • A probability calculated in both tails of a distribution is called a two-tailed probability (see Figure 2).
  • Should the one-tailed or the two-tailed probability be used to assess Mr.
  • Statistical tests that compute one-tailed probabilities are called one-tailed tests; those that compute two-tailed probabilities are called two-tailed tests.
  • The upper (right-hand) tail is red.

• Directional Hypotheses and One-Tailed Tests

  • The vast majority of hypothesis tests involve either a point hypothesis, two-tailed hypothesis or one-tailed hypothesis.
  • If the test statistic is always positive (or zero), only the one-tailed test is generally applicable, while if the test statistic can assume positive and negative values, both the one-tailed and two-tailed test are of use.
  • Two-tailed tests are only applicable when there are two tails, such as in the normal distribution, and correspond to considering either direction significant.
  • For a given test statistic there is a single two-tailed test and two one-tailed tests (one each for either direction).
  • A one-tailed test, showing the $p$-value as the size of one tail.