# Variables and Data A variable contains data about anything we measure. For example; age or gender of the participants or their score on a test.

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1 The Analysis of Research Data The design of any project will determine what sort of statistical tests you should perform on your data and how successful the data analysis will be. For example if you decide to interview five students, using an unstructured interview technique, to ask what they feel about a particular thing or you decide to observe four people in a particular setting it would be very difficult to obtain numerical data from the observation or from the unstructured interviews it would be better to use qualitative data analysis techniques. In the reverse if you are collecting data from 2000 patients using results from laboratory tests or data using questionnaires (which produce numerical data), it would be very difficult to report your findings in a descriptive manner using verbal quotations. It would be better to use statistical data analysis methods. However, you can use a mixture of the two methods. For example, using questionnaires that give the respondents the opportunity to make comments or describe their experiences as well as responding to questions from a fixed set of answers. Variables and Data A variable contains data about anything we measure. For example; age or gender of the participants or their score on a test. Variables can contain two different types of data; categorical data and continuous data. Categorical data Categorical data is a measure of type rather than amount and can be broken down into nominal data and ordinal data. Nominal data is data that is assigned to categories or labelled e.g. male / female, or a long string of data where the number is randomly assigned. E.g. post code, nationality, television channels etc. The categories or labels cannot be ordered or ranked and are not related to each other. Ordinal data is data where numbers have been used to put objects in an order. It is categorised in a fixed, specific order and we can only say one thing is more or less than something else on the scale. For example, income band rating scales where someone on the lowest band earns less than someone on the highest. Although the data can be ranked in order it does not imply that they are at equal intervals between categories e.g. the different between the lowest and the middle scale may not be the same as the difference between the middle scale and the highest scale. Continuous data Continuous data is numerical data with equal intervals between the data e.g. the distances between the scores is the same. Continuous data can be further broken down into interval and ratio data Interval data is when the differences on each point of the scale is the same, however, 0 is a marker on a scale rather than a true zero e.g. temperature 0oC does not imply there no temperature at all! (absolute 0)

2 Ratio data is when the data has a true 0 e.g. number of children 0 = no children. Other examples of ratio data include time, height, levels of anxiety. Level of Property measurement Categories Ranks Equal intervals True zero point Nominal Yes No No No Ordinal Yes Yes No No Interval Yes Yes Yes No Ratio Yes Yes Yes Yes How to Analyse Your Data 1. Descriptive Statistics Descriptive statistics allow the researcher to; Get an overview of the data Check for any missing data Look at the range of answers or data they have collected Identify unusual cases and extreme values Identify obverse errors in the data Types of tests that can be used on different data types Nominal data Frequency tables Bar charts Pie charts Percentages Ordinal data Frequency tables Percentages Bar charts Median Interval or Ratio data Histograms Mean Median If data is missing; 1 st check if the data was missed when entering the data onto the database. If the data was not collected you have several options; You can delete the case from any further analysis either, just for the variables where the data is missing or delete the case completely. If a lot of the data for one patient is missing (e.g. about 20%) it may be best to delete the case completely to avoid this case effecting your overall results. You can put in the mean value for that case ( see measures of central tendency). Use the fact that the data is missing as a finding in itself. For example, the percentage of blood tests not taken. If there is an outlier (E.g. a person scoring much higher than everyone else. This outlier may affect your findings and it may help to delete outliers from your analysis. Always sate what you have done to the data to address these issues when writing up your findings. Checking for normality One of the criteria for using some statistical tests (parametric tests, such as t-tests) is that the data in your variables is normally distributed. To check if your data is normally distributed you can either; Look at the skewness and kurtosis values. Skewness measures the degree to which cases are clustered towards one end of the distribution. Kurtosis measures the peakedness of a distribution. The closer the values are to 0 the more likely they are normally distributed, scores of 5 or more indicate skewed data.

3 Calculate the z scores for the data: The Z score computes a standardised score, which indicates how many standard deviations above or below the sample mean your score is. This is calculated by- Z score = Case score sample mean Standard deviation Look at the histograms for each variable, the data should ideally look like this; If your data is only slightly skewed away from a normal distribution you can use transformation procedures (it may help to see a statistician for this) or you should use statistical tests (non-parametric tests) that do not require a normal distribution. Measures of Central Tendency Describing the pattern of your data can help you to understand what it means. This can be done by calculating a measure of central tendency, either the mean, median and / or mode Mean The mean is the average value of the data in a variable i.e. the sum of all the cases divided by the total number of cases. This is the best measure to use if your scores have a normal distribution. Median This is the middle score (50 th percentile). If that data was split in half in numeric order this would be the mid point score. This is a useful measure when the data is skewed i.e. there are a high number of low scores. The group or number that occurs most frequently. Measures of dispersion Measures of dispersion are statistics designed to describe the spread of scores around a measure of central tendency Minimum and Maximum The lowest (smallest) and the highest (largest) values. Range The difference between the maximum and the minimum values. Variance An overall measure of how clustered the data values are around the mean. The variance has the disadvantage of being the wrong units as it is the mean squared difference between each score and the mean of those scores.

4 Standard deviation The standard deviation takes all the observed values into account and is the square root of the variant. This restores the variant back into its original units. Appropriate measures of dispersion for each type of data Nominal data None Ordinal data Minimum Maximum (range) Variance Standard Deviation Scale data Minimum Maximum (range) Variance Standard Deviation You can use frequencies to describe your sample e.g. number or percentage of males and females when writing up you findings. It also helps to use the measure of central tendency and dispersion to further describe your sample e.g. mean and standard deviation of age and length of illness. 2. Inferential Statistics Inferential statistics look at whether there are any relationships or differences between variables that are genuine and not due to chance. Analysing combinations of categorical and continuous data There are two types of statistical tests that can be used to analyse data. These are the parametric tests and the non-parametric tests. Parametric tests are performed on data that is normally distributed and non-parametric tests are performed data that do not conform to a normal distribution. Choosing which statistical test to use; Think about whether you are looking for a difference, a relationship, a pattern between variables, predict an outcome or to test the robustness of a scale. Then look at which test would best suit your data depending on its type e.g. interval data, whether the data is from the same group of participants such as data pre and post intervention (related samples) or different groups such as patient and nurse groups (unrelated samples). Tests of Difference between two groups Interval Data Related Samples Related samples t-test Unrelated Samples - Unrelated samples t-test Ordinal Data Related Samples Wilcoxon test Unrelated Samples Use a Mann Whitney U test Nominal Data Related Samples McNemar change test Unrelated Samples - Chi-squared test Tests of Difference between more than two groups Interval Data Related Samples Repeated Measures ANOVA Unrelated Samples - One-way ANOVA If there are two or more variables in both groups use a MANOVA Ordinal Data Related Samples Freidman Unrelated Samples - Kruskall-Wallis

5 Nominal Data Use a complex chi-square Information Sheet 5 Relationships between variables e.g. job satisfaction and productivity Interval Data Pearson s product moment coreelation co-efficient Ordinal Data Spearman rank correlation co-efficient Nominal Data Phi co-efficient Predicting an outcome e.g. predicting quality of life from levels of pain If you have one interval predictor variable and one interval outcome variable = Simple regression If you have more than one interval/ordinal/nominal predictor variable and one interval level outcome variable = Multiple regression If you have more than one interval, ordinal or nominal predictor variables and one nominal or ordinal level outcome variable = Logistic regression If you have more than two interval level predictor variables and a ordinal or nominal outcome variable = Discriminant function analysis Testing the robustness of a scale. To examine correlations between scales and produce a reliability co-efficient = Alpha reliability analysis To check the underlying factor structure of a scale in comparison to its established factor structure = Confirmatory factor analysis To check the underlying factor structure of a scale If the underlying factor structure of a scale is unknown = Exploratory factor analysis Significance The majority of statistical tests will provide a p value this can be used to indicate the statistical significance of the results and the degree to which we can be confident that the results are not due to chance. There are different levels of significance that indicate different levels of confidence, P<0.05 this indicates that we can be 95% confident that our findings are not due to chance. P<0.01 this indicates that we can be 99% confident that our findings are not due to chance. This is a stronger result. For example if a p value = 0.04, this value is < 0.05 but not <0.01 and therefore we would state that this finding is significant at the P<0.05 level. Alternatively, If the p value = 0.17 this is not less that the suggested significance levels and therefore the findings would not be significant. Hypothesis Testing It is common practice to state two hypotheses, when designing a research study the null hypothesis and the alternate/experimental hypothesis. The null hypothesis (Ho) states there is no difference / relationship between variables and any differences are purely by chance. The Alternate hypothesis (H1) states that there is a difference / relationship between variables that is not due to chance. After using the appropriate statistical tests you can then either be able to reject the Ho or accept it depending on your results. Type 1 and Type 11 Errors When making a decision about whether or not to reject the hypothesis (Ho) there is always a possibility of making the wrong decision. (The likely hood of coming to the wrong conclusion is equal to the level of confidence, for example this would be 5% at the 0.05 confidence level). This should be acknowledged. The more tests you perform the greater error level.

6 Accepting / rejecting the null hypothesis possible outcomes. Decision of researcher True population situation Ho is true H1 is true Accept Ho OK Type 11 error Reject Ho Type 1 error OK Don t forget it always helps to discuss your data with other researchers! March 2006

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