STATISTICAL ASSIGNMENT
Assignment
The following assignment examines the usage of measures of central tendency in two scientific research reports.
Measures of Central Tendency
Measures of Central Tendency are used in data analysis when we want to know how the data cluster around some central value. Most commonly used central values are represented by the mean, median and mode; The extent of deviation from the centrally located value is represented by variance, standard deviation, inter-quartile range, or tabulation of all the frequencies. Central tendency differs depending on the level of measurement.
This report analyses how Mean and Standard Deviation were used to describe the research results.
Brief Summary of the Studies
Study 1
The aim of this study was to compare the acute hemodynamic responses during high-intensity intermittentexercise (HIIE) session compared with moderate-intensity continuous exercise (MICE) session in patients with heart failure and reduced ejection fraction (HFREF). So, the dependent variable is acute hemodynamic responses while the variables being studied: high intensity intermittent exercise vs moderate intensity continuous exercise MICE.
Study 2
The aim of the study was to study the impact of clear speech, increased vocal intensity and rate reduction on acoustic characteristics of vowels in patients with Multiple Sclerosis, Parkinson’s Disease and healthy control patients. The speakers were made to read sentences in clear, loud and slow as well as usual conditions and magnitude production was used to generate differences in the clearness, the intensity and rate of speech. The values for the peripheral and non peripheral vowels were generated at different percentages of vowel duration to obtain static and dynamic acoustic measures.
How Central Measures were used in these studies
Study 1
Categorical variables include sex, age was described in terms of frequencies and percents
Continuous variables include variables such as exercise time, power output, oxygen and carbon dioxide output, parameters related to measurement of ventilator level, Mean and Standard Deviation were used to denote the measures of central tendency and were used for continuous variables. One way ANOVA was used to calculate the p values for the hemodynamic comparisons. Repeated ANOVA was used for comparing the kinetics during High Intensity and Moderate Intensity Exercise.
Study 2
For the Sentence Intelligibility Scores and Scaled Speech Severity analysis of the patients, both mean and standard deviation were used to measure the average value and the extent of deviation from t he mean. ANOVA was used for measuring the group difference in scaled severity. Pearson product moment correlations and absolute measurement errors were used to index reliability. Because a number of variables were studied, multivariate analysis was carried out to generate a fit with the dependent variables in the repeated measures design. Each measure was a fit of group, condition and group x condition interaction. Gender and habitual condition was included as covariates for segment level measures. P value of <0.05 was used for determining statistical significance.
Explanation of how this is appropriate or inappropriate
Study 1
These measures were appropriately used for the location of a central value as well as to understand the spread of values as mean and Standard Deviations can only be used with variables whose values are in the interval/ratio measurement level and not with variables having ordinal or nominal levels of measurement such as categorical variables, for which mode, median and interquartile range may be used to represent the spread and central value.
Study 2
The use of Standard Deviation and Means for this study is appropriate as the variables being studied are continuous variables of interval/ratio.
Where the assumptions of measures of central tendency met or not?
The different measures of central tendency are best suited in certain situations and are not applicable for each situation. For e.g. the mean is the one of the most popular widely used measures of central tendency as it represents a model of your data set and represents every single value in the data set and it is also the value which would produce the least amount of error as compared to the other values but the problem with the usage of mean it is liable to get skewed when there are extreme values in the data sets ( i.e. when outliers are there) i.e. there are unusually large and small values in the data set and when the data set consists of such extreme values and there is skew in the frequency distribution, a better measure of central tendency should be chosen such as median.
In case of Study 1 and 2, the assumptions were met and the results did not seem to indicate any major flaw or skew in the data set.
Use of Anova:
For the use of one way ANOVA as a measure of variance, the stipulations are that all the values in the groups being analysed should be following a normal curve with different population averages being okay and but with the Standard Deviations being equal. ANOVA may give wrong results if the groups are not following the normal distribution curve. The largest sample SD should not be larger than twice the smallest.
All the requirements were met as the data set did not seem to show major discrepancies and extremeties. In fact, for Study 2, the Standard Deviations were much lesser, which pointed towards more accuracy of the data.
Levels of measurement of variables in the study
Several levels of measurement of variables were identified including both nominal, interval/ratio as well as categorical and continuous variables.
Study1
Nominal variables include age, sex, disposition to diseases, use of devices, medications taken, risk factors. Interval/ratio variables include those which are used for measuring Gas exchange and central hemodynamic parameters (cardiac bioimpedance) such as stroke volume (SV), oxygen uptake, cardiac output (CO), and arteriovenous difference (C(a-v)O2) were compared.
Study 2
Dependent variables were expressed as difference measures. The dependent variable was effect on acoustic differences and the independent variables being tested were clear speech, increased vocal intensity, rate reduction and the parameters which were used to describe each of these such as articulary rate, sound pressure etc all as a function of group and condition. There were three levels of variables used here: control, patients with multiple sclerosis and patients with Parkinson’s disease.
Were the levels of measurement of the study variables appropriate?
Study 1 The variables selected were very appropriate as they gave a comprehensive descriptive analysis of the data set. There were the different categorical variables to describe the patient population used for the studies. The list of parameters used for conducting the effect of exercise on hemodynamics were varied and were of the continuous variable class. The complete picture of the health condition of the patients, following the exercises could be studied.
Study 2 The levels of measurement of study variables were quite appropriate as most of the parameters used for determining the effect on acoustic differences are of continuous nature.
How the data was displayed (i.e., graphs, tables) and was it appropriate?
Study 1
The data from the maximal cardiopulmonary tests, hemodynamics tests and effect of the moderate and high intensity exercise on hemodynamics were displayed in a tabulated fashion. Data of the baseline parameters of the patients, before the conduction of the experiment was also displayed. The parameters as well as the mean values with the Standard Deviations were listed alongside. In a legible way. Undashed Line graphs of the hemodynamic kinetics during maximal cardiopulmonary exercise showing the effect on cardiac output, stroke volume and oxygen levels were very clear and showed that the errors bars were within the same range for all the data values. As such error bars indicate the level of confidence in the data. If there is a large discrepancy in the data values from the mean, you will have larger error bars and less confidence on the data values. In this case, the error bars in the data are wide enough to indicate there is some kind of deviations from the mean in the data values but then as the level of error is same across in all the three conditions studied, it may be considered okay for this purpose. But more experiments with a more larger data set may need to be done, which can generate more confident data. Line graphs of the effect of moderate and high intensity exercise on the hemodynamics were also quite relevant and useful
Study 2
It made used of extensive representation of the data obtained in the form of tables as well as graphs. The tables showed the mean and the Standard Deviation values for the different independent variables studied in different conditions (habitual, slow, loud and clear) and in different groups (Control and the two test) Bar graphs, not showing error bars, were used to show certain comparative data. Error bars were not shown as they would distract from the comparisons.
Conclusion
In summary, Measures of Central Tendency help to describe the data obtained from research studies and identifies the most common values as well as how much of spread occurs, which helps us in analyzing the data obtained from population studies.
References
Central hemodynamic responses during acute high-intensity interval exercise and moderate continuous exercise in patients with heart failure. (2012). Applied Physiology, Nutrition & Metabolism, 37(6), 1171-1178. doi: 10.1139/h2012-109
Kwan Ho Chui, K. (2012). Descriptive Statistics - SSSI - Confluence. [online] Retrieved from: https://wikis.uit.tufts.edu/confluence/display/SSSI/Descriptive+Statistics [Accessed: 11 Apr 2014].
Math.colgate.edu. (2014). The Assumptions for One-Way ANOVA. [online] Retrieved from: http://math.colgate.edu/math102/dlantz/examples/ANOVA/anovahyp.html [Accessed: 11 Apr 2014].
Ncsu.edu. (2014). Using Descriptive Statistics. [online] Retrieved from: http://www.ncsu.edu/labwrite/res/gt/gt-stat-home.html [Accessed: 11 Apr 2014].
Onlinestatbook.com. (2014). Measurement Demonstration. [online] Retrieved from: http://onlinestatbook.com/2/introduction/measurement_demo.html [Accessed: 11 Apr 2014].
Polsci.wvu.edu. (2014). Levels of Measurement. [online] Retrieved from: http://www.polsci.wvu.edu/duval/ps601/Notes/Levels_of_Measure.html#Tools of Inference [Accessed: 11 Apr 2014].
www.sagepub.com. (2014). Appendices: Guide for selecting appropriate inferential and descriptive. [online] Retrieved from: http://www.sagepub.com/fitzgerald/study/materials/appendices/app_a.pdf [Accessed: 11 Apr 2014].
Tjaden, K., Lam, J., & Wilding, G. (2013). Vowel Acoustics in Parkinson's Disease and Multiple Sclerosis: Comparison of Clear, Loud, and Slow Speaking Conditions. Journal Of Speech, Language & Hearing Research, 56(5), 1485-1502. doi:10.1044/1092-4388(2013/12-0259)
