Data Analysis

Normal Distribution

The idea of normal distribution is that, for a given attribute, like scores on a test, most of said scores will be the mean or around the mean. Decresing scores will be further away from the mean. Normally distributed data is symmetrical; when it is plotted on  graph, it makes an even bell shapeed curve. The same amount of scores above the mean will be below it as well with normal distribution.

Skewed Distribution

Skewed distribution is when there is an uneven amount of scores above or below the mean value. A positive skewed distribution is when there is an extreme high score and negative is when there is an extreme low score. A positive skewed distribution will have more low than high scores because the skew has been caused by an outlying high score. A negative skewed distribution will have more high scores than it will low scores because the skew has been caused by an outlying low score. .

Percentages

Percentages are a descriptive statistic that shows the rate, number or amount of something per 100 of something. Percentages can be plotted on a pie chart to show data. Data can be converted into a percentage by multiplying them as a factor of 100. If you were to have a scpore of 67 out of 80 on a test and wanted to calculate the percentage score, you would have to divide 67 by 80, giving you 0.8375, then multiply it by 100 to give you a percentage, the answer would be 83.75%. You can use percentages for many different things like efficiency of a drug used for a mental illness. Percentages can be used in bar charts as well as pie charts. 

Correlational Data

Correlational studies provide that data can be expressed as a correlation coefficient, either showing as a positive correlation, negative correlation or no correlation. The stronger the correlation, the closer that it will be ti either +1 or -1. Correlational data is plotted on a scattergram, which best indicates it's correlational strength or weakness and its correlational direction. 

The Mean 

The mean is the mid-point  of all combined values of a set of data, being calculated by adding all of te scores from a set of data together and the dividing by the total number of scores. We use the mean to calculate averages of scores when there is a lot of data. Using the mean is good because it is the most accurate measure of central tedancy; it uses the interval level of measurement (where the units are of equal size). However, the mean can be less useful if the scores collected are skewed, meaning if there are some large and some small results it can throw the average. 

The Median 

The median is the middle score of a set of rank ordered scores. The median will always be the middle number if there is an odd amount of scores, but if there is an even amount of scores, the median will be a mid-point between two scores. This means that it may not be oe of the original numbers that were there. The median can be used to remove disproportionally high or low score by finding the middle ground of a set of data. The median is good for use in results because the median is not affected by large 'freak' scores, but the median is not as sensitive as the mean, because not all the scores are used in the calculation. 

The Mode

The mode is the value which comes up the most or is most common in a set of scores. The mode can be used to determine the most common result in a set of data. The mode is less prone to distortion by extreme values, unlike the mean, but there can be more than one mode in a set of data, which can be unhelpful. 

The Range

The range is calculated by subtracting the lowest value from the highest value in a set of data. For example, if ou have data the goes from 13 - 40, you would take 13 away from 40. This gives you 27, which would be your range. you can use the range when yiou are trying to calculate the gap between your higest and lowest score, which can help you analyse your data better. Using the median is fairly quick and easy, which is a good advantage when you don't have much time. Despite this, the range can be distorted by 'freak' values much like the mean can be.

Standard Deviation

Standard deviation is a measure that shows the variability or spread of a set of scores from the mean. The larger the standard deviation, the more far spread the scores will be. Standard deviation is calculated by first calculating the mean of the scores, subtracting the mean from each individual score and then squaring the answers. After this, you must add all of these values together. Devide this sum by the number of score minus one. This is the variance. Using a calculator, to work out the square root of the variance. This answer is standard deviation. an advantage of standard deviation is that it is a more sensative dispersion measure than the range since all of the scores are used in its calculation. A disadvantage of it is that it is waaaaaaaay more complicated to work out than other things. 

Bar Charts

Bar charts show data in the form of different catagories. These catagories are presented on the x axis of the charts, with even gaps between each of the bars. The bars should also be of the same width. The gaps represent the fact that not all data on the chart is continuous. Bar charts can only show one value of data - totals, means, percentages or ratios. Each bar can only represent one catagory and one value. The y axis of the bar chart should show the average.

Histograms

Histograms are very simlar to bar charts, but the main differene is that the bars on histograms represent continuous data. This means that the bars aren't always the same size. You have to calculate the frequency density in the table to be able to draw the histogram. There is no space between the bas on this graph because the data is contnuous wich is conveyed by the lack of space.

Frequency Polygons

Frequency polygons have the data placed on the x-axis and it is continuous much like histograms. The polygon is made by placing a point in the middle of each bar of the histogram. This means that more frequency distributions can be shown on the same graph, which is advantageous.

Pie Charts

Pie charts are used to show the frequency of categories using percentages. Fpr each percentage, the pie chart is split into representative sections. Each section epresents a value. The different sections are also colour coded in relation to the categories.

Tables

Tables of results summarise the findings of data from experiments and studies. The differ from data tables, which show all f the results frm a study. The results in a data table are raw data and have not gone throgh any statistical analysis yet. In results tables, you have to represent data through totals or percentages in addition to measures of central tendancy and dispersion.