Statistics Essays | Analysis of Data

Statistics Essays Analysis of DataConsider and discuss the required approach to analysis of the selective information fall provided.As part of this look also how you would test the supposal below and explain the reasons for your decisions. Hypothesis 1 Male children are lankyer than female children. Null hypothesis There is no battle in height amidst male children and female children. Hypothesis 2 Taller children are heavier. Null hypothesis There is no relationship between how tall children are and how much they weigh.Analysis of data setThe data set is a list of 30 childrens gender, age, height, the data weight, upper and lower limb lengths, bosom colourise, like of cocoa or not andIQ.There are two main things to consider before and the data. These are the types of data and the quality of the data as a sample.Types of data could be nominal, ordinal, interval or proportionality.Nominal is also know as categorical. Coolican (1990) gives more details of all of these and his definitions have been used to decide the types of data in the data set.It is also helpful to distinguish between continuous numbers, which could be measured to any number of decimal places an discrete numbers such(prenominal) as integers which have finite jumps like 1,2 etc.GenderThis variable can only distinguish between male or female.There is no smart set to this and so the data is nominal.AgeThis variable can sign integer values. It could be measured to decimal places, but is generally only recorded as integer. It is ratio data because, for example, it would be meaningful to say that a 20 year old person is twice as old as a 10 year old.In this data set, the ages range from 120 months to 156months. This needs to be consistent with the population being tested.HeightThis variable can take values to decimal places if necessary. Again it is ratio data because, for example, it would be meaningful to say that a person who is 180 cm tall is 1.5 times as tall as someone 120cmtall. In this sample it is measured to the nearest cm.WeightLike height, this variable could take be measured to decimal places and is ratio data. In this sample it is measured to the nearest kg.Upper and lower limb lengthsAgain this variable is like height and weight and is ratio data.Eye colourThis variable can take a limited number of values which are eye colours. The order is not meaningful. This data is therefore nominal(categorical).Like of chocolate or notAs with eye colour, this variable can take a limited number of values which are the sample members preferences. In distinguishing hardly between liking and disliking, the order is not meaningful. This data is therefore nominal (categorical).IQIQ is a scale measurement embed by exam each sample member. As such it is not a ratio scale because it would not be meaningful to say, for example, that someone with a score of one hundred twenty-five is 25% more intelligent than someone with a score of 100.There is another level of data me ntioned by Cooligan into which none of the data set variables fit. That is ordinal Data. This means that the data have an order or rank which makes sense. An example would be if 10students tried a test and you recorded who finished quickest, 2ndquickest etc, but not the actual time.The data is intended to be a sample from a population about which we can make inferences. For example in the hypothesis tests we deprivation toknow whether they are indicative of population differences. The results can only be inferred on the population from which it is drawn it would not be valid otherwise.Details of sampling methods were found in Bland (2000). To accomplish the required objectives, the sample has to be representative of the defined population. It would also be more accurate if the sample is stratified by known factors like gender and age. This means that, for example, the proportion of males in the sample is the same as the proportion in the population.Sample size is another considera tion. In this case it is 30.Whether this is adequate for the hypotheses being tested is examined below.Hypothesis 1 Male children are taller than female children.Swift (2001) gives a very readable account of the hypothesis testing process and the structure of the test.The first step is to set up the hypothesesThe Null hypothesis is that there is no difference in height between male children and female children.If the alternate(a) was as Coolican describes it as we do not predict in which direction the results will go then it would have been a two-tailed test. In this case the alternative is that males are taller it is therefore a specific direction and so a one-tailed test is required.To test the hypothesis we need to set up a test statistic and then either match it against a pre-determined critical value or calculate the probability of achieving the sample value establish on the assumption that the null hypothesis is true.The most commonly used significance level is 0.05. Accordin gto Swift (2001) the significance level must be clear-cut before the data is known. This is to stop researchers adjusting the significance level to get the result that they want rather than accepting or denying objectively.If the test statistic probability is less than 0.05 we would reject the null hypothesis that there is no difference between males and females in favour of males being heavier on the one sided basis.However it is possible for the test statistic to be in the rejection zone when in fact the null hypothesis is true. This is called a TypeI misplay.It is also possible for the test statistic to be in the acceptance zone when the alternative hypothesis is true (in other words the null hypothesis is false). This is called a Type II break. Power is 1 -probability of a Type II error and is therefore the probability of correctly rejecting a false null hypothesis. Whereas the Type I error is set at the desired level, the Type II error depends on the actual value of the alt ernative hypothesis.Coolican (1990) sets out the possible outcomes in the following table