Descriptive Statistics - Thiyagu K
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The document outlines key concepts in descriptive statistics related to quantitative variables, focusing on measures of central tendency, variability, and distribution shape. It details methods for assessing normality, including the Kolmogorov-Smirnov and Shapiro-Wilk tests, and explains various visualizations for data analysis such as histograms and box plots. Additionally, it provides guidelines for using SPSS software for statistical analysis and interpreting the results related to data distribution.
Descriptive Statistics - Thiyagu K
- 1. K.THIYAGU, Assistant Professor, Department of Education, Central University of Kerala, Kasaragod Descriptive Statistics
- 2. When summarizing quantitative (Continuous/Interval/Ratio) variables, We are typically interested in asking 4 questions like:
- 3. What is the "center" of the data? Mean & Median
- 4. Measures of Central Tendency •The average value of the distribution Mean •The middle value of the distribution Median •The most frequently occurring value Mode
- 6. How spread out is the data? QD & SD
- 7. What are the extremes of the data? Minimum, Maximum; Outliers
- 8. Measures of Variability • The Range • The Average Deviation • The Standard Deviation • The Quartile Deviation
- 10. What is the "shape" of the distribution? Is it symmetric or asymmetric? Skewness, Kurtosis
- 11. Skewness Right Skewed: Skewness > +1.0 Normal Probability Curve Skewness = -1 to +1 Left Skewed: Skewness < -1.0 Kurtosis Leptokurtic: Kurtosis > +1.0 Mesokurtic: Kurtosis = -1 to +1 Platykurtic: Kurtosis < -1.0 Measures of the shape of the distribution Interpretation for the Psychometric Purposes A Skewness & kurtosis value of +/-1 is considered very good for most psychometric uses, but +/-2 is also usually acceptable.
- 12. Skewness
- 13. Kurtosis
- 14. Data Screening Distribution Diagnosis • Frequency tables • Histograms and bar graphs • Stem-and-leaf plots • Box plots
- 15. Frequency Tabulation and Percentage are useful for Categorical Data Analyze Descriptive Statistics Frequencies
- 17. Descriptive Statistics SPSS N valid responses Mean Sum Standard deviation Variance Minimum Maximum Range Standard Error of the mean Skewness Kurtosis
- 18. • This is the number of non-missing valuesValid N (listwise) • This is the number of valid observations for the variable.N • Minimum, or Smallest, value of the variable.Minimum • Maximum, or Largest, value of the variable.Maximum • MaximumMaximum • Average of the observations (CT)Mean • Square root of the variance. It measures the spread of a set of observations.SD • It is the sum of the squared distances of data value from the mean divided by the variance divisor.Variance • Skewness measures the degree and direction of asymmetry. NPC = Skewness = 0Skewness • Kurtosis is a measure of tail extremity reflecting either the presence of outliers in a distribution or a distribution’s propensity for producing outliersKurtosis
- 20. Tests of Normality •Claim: •H0: The data come from the specified distribution; •H1: The data do not come from the specified distribution •It technically can be used to test if the data come from a known, specific distribution (not just the normal distribution). Kolmogorov- Smirnov (K-S) (Non-Parametric Test) •Claim: •Ho: The sample was drawn from a normal distribution. •H1: The sample was not drawn from a normal distribution Shapiro-Wilk (Parametric Test) The Shapiro-Wilk Test is more appropriate for small sample sizes (< 50 samples), but can also handle sample sizes as large as 2000.
- 21. If p < Significant Level of Alpha () Or p < 0.05 / 0.01 Reject the null hypothesis. There is sufficient evidence that the data is not normally distributed. If p > Significant Level of Alpha () Or p > 0.05 / 0.01 Do not reject the null hypothesis. There is not enough evidence to conclude that the data is non-normal. Tests of Normality Criteria to Reject or Not Reject the Null Hypothesis:
- 22. Running the Procedure - SPSS Analyze Descriptive Statistics Explore Add Variables •Dependent List box Plots •Normality plots with tests. •Continue. Options •Exclude cases pairwise. •Continue
- 23. Normal Q-Q Plot In order to determine normality graphically, we can use the output of a normal Q-Q Plot. If the data are normally distributed, the data points will be close to the diagonal line
- 28. Median (Q2/50th Percentile): The middle value of the dataset. First Quartile (Q1/25th Percentile): The middle number between the smallest number (not the “minimum”) and the median of the dataset. Third quartile (Q3/75th Percentile): The middle value between the median and the highest value (not the “maximum”) of the dataset. Interquartile Range (IQR): 25th to the 75th percentile. whiskers (shown in blue) outliers (shown as green circles) “Maximum”: Q3 + 1.5*IQR “Minimum”: Q1 -1.5*IQR
- 30. Tooltip Description Procedure Open data document Open a datafile File > Open > Data. Save this document Save the active dataset File > Save or Ctrl + S. Print Print the contents File > Print. Undo Back to Previous Edit > Undo or Ctrl + Z. Redo Equivalent to Edit > Redo or Ctrl + Y. Go to case Jump to a specific case (row) Edit > Go to Case Go to variable Jump to a specific variable (column) Edit > Go to Variable. Variables View the variable name etc. Utilities > Variables. Find Search for a value in the dataset Ctrl + F Replace Replace a value in the dataset. Ctrl + H, Insert cases Insert a case between two existing cases. Edit > Insert Cases. Insert variable Insert a new variable between two existing variables Edit > Insert Variable. Split file Stratify your analyses based on a categorical variable Data > Split File. Select cases Extract a set of cases to a new datafile based on some criteria, or apply a filter variable. Data > Select Cases. Value labels Toggle whether the raw data or the value label is displayed in the Data View window View > Value Labels.
- 34. Thank you