# Research Paper: Inferential Statistics to Evaluate Sample

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SAMPLE EXCERPT:

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Note that the two hypotheses we propose to test must be mutually exclusive; i.e., when one is true the other must be false. And we see that they must be exhaustive; they must include all possible occurrences. Lastly, the researcher must translate the research hypothesis into operational terms. The researcher goes on to operationally define fast tempo as being music at a tempo of 120 bpm (beats per minute) and slow tempo music as being music at a tempo of 60 bpm. In addition, a researcher has to specify how participants are going to rate the music for happiness (Hays, 1973).

8. Discuss probability in statistical reference, as well as the meaning of significance.

Probability is the likelihood of the occurrence of some event or outcome. A significant result is one that has a very low probability of occurring if the population means are equal. The probability required for significance is called the alpha level and is often .05. All results obtained by statistical methods suffer from the disadvantage that they might have been caused by pure statistical accident. The level of statistical significance is determined by the probability that this has not, in fact, happened. P is an estimate of the probability that the result has occurred by accident. Therefore a large value of P. represents a small level of significance (Moses, 1986).

In experiments one needs to define a level of significance at which a correlation will be deemed to have been proven, though the choice is often actually made after the event. It is important to realize that, however small the value of P, there is always a finite chance that the result is a pure accident. A typical level at which the threshold of P. is set would be 0.01, which means there is a one percent chance that the result was accidental. The significance of such a result would then be indicate by the statement P<.01.

Unfortunately it has become customary to operate with lower levels of significance. A level frequently quoted is P<.05. This means that there is a one in twenty chance that the whole thing was accidental. This is particularly worrying in areas that are newsworthy or politically correct, since it is likely that more than twenty similar experiments are being conducted worldwide, so it is almost certain that there will be one positive result, whether the correlation is genuine or not. Because negative results are almost never published this means that an unknown but possibly large number of false claims are sustained (Tijms, 2004).

Sources:

Ader, H.J., Mellenbergh, G.J. & Hand, D.J. (2007). Advising on research methods: A consultant's companion. Johannes van Kessel Publishing: Huizen, The Netherlands.

Fisher, R.A. (1966). The design of experiments. 8th edition. Hafner: Edinburgh, Scotland.

Hays, W. (1973) Statistics for the Social Sciences. Holt, Rinehart and Winston: London, UK.

Moses, L.E. (1986) Think and Explain with Statistics, Addison-Wesley: New York: NY.

Tijms, H. (2004). Understanding…
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