Statistical analysis
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The document discusses statistical analysis and concepts such as standard deviation, normal distribution, and t-tests. It provides examples of how to calculate and interpret standard deviation to understand the variation in data compared to the mean. It also explains how a t-test can be used to determine if there is a statistically significant difference between the means of two samples by taking into account the means, standard deviations, and population sizes.
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This document discusses various methods for summarizing data, including measures of central tendency, dispersion, and categorical data. It describes the mean, median, and mode as measures of central tendency, and how the mean can be affected by outliers while the median is not. Measures of dispersion mentioned include range, standard deviation, variance, and interquartile range. The document also discusses percentiles, standard error, and 95% confidence intervals. Key takeaways are to select appropriate summaries based on the data type and distribution.
Properties of Standard Deviation
The document discusses standard deviation and its properties. Standard deviation is a measure of how spread out numbers are from the average (mean) value. It is always non-negative and can be impacted by outliers. A low standard deviation means values are close to the mean, while a high standard deviation means values are more spread out. Standard deviation can be used to calculate what percentage of data falls within certain intervals from the mean when data is normally distributed.
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This document discusses various statistical concepts for summarizing and analyzing quantitative data, including:
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- Correlational research which investigates relationships between two variables using the Pearson correlation coefficient.
Machine learning session1
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Statistics for ess
1. The document discusses statistical analysis techniques for describing and comparing data sets, including calculating the mean, standard deviation, and using t-tests.
2. It explains how to calculate the mean and standard deviation of data sets to analyze the central tendency and variability. The standard deviation summarizes how tightly values cluster around the mean.
3. T-tests are used to determine if differences between two data sets are statistically significant by comparing the means relative to the standard deviations and considering the degree of overlap between the sets.
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Statistical analysis
- 7. This variation can be shown using a frequency distribution graph
- 8. The mean value is in the middle of the distribution
- 10. 95% of the data is within 2 SD from the mean
- 14. 68% of data is +/- 1SD, so 68% are between 2.0cm and 3.0cm
- 16. Starter In a population of men the systolic blood pressure shows a normal distribution. The mean of the population is 125 (measured in mm and Hg) and the standard deviation is 10. If the population was 1000, how many of them have a blood pressure between 115 and 135mm Hg? 680 men have blood pressure between 115 and 135mm Hg. If the mean is 125, and the standard deviation is 10, then +1 Sx is 135, and -1 Sx is 115, and we know that 68% of your data (in this case the men) are +/-1 Sx from the mean.
- 18. Find the mean of your data
- 23. Means A = 10 B = 20
- 24. Means A = 10 B = 20 Is there a significant difference between the means?
- 25. Means A = 10 B = 20 Is there a significant difference between the means?
- 26. Means A = 10 B = 20 Is there a significant difference between the means? Would knowing the standard deviations help? What if both had “large” standard deviations?
- 27. Means A = 10 B = 20 Is there a significant difference between the means? Would knowing the standard deviations help? What if both had “small” standard deviations?
- 28. Means A = 10 B = 20 Is there a significant difference between the means? Would knowing the population size help? What if one had a large population size and the other a small size? What if both were large or both small?
- 29. The t-test takes from both samples: the means, the standard deviations and the population size into account and will give you a t-value which you can use with a t-test table to determine if there is a statistically significant difference between the means. DO NOT learn the formula. The t-value will be given to you.
- 32. Calculated Value of t > critical value it has is <0.05 which means there is a significant difference
- 34. H0 Null Hypothesis states that there is no significant difference between the two groups Never want to assume there is a difference The null hypothesis typically corresponds to a general or default position. For example, the null hypothesis might be that there is no relationship between two measured phenomena or that a potential treatment has no effect.