Examining Samples Numerically PDF

2/12/25, 11:55 AM OneNote Examining samples Numerically Tuesday, January 28, 2025 9:32 AM Examining samples: You have your data, now need to look at it- does it look ok? ○ Possib...

2/12/25, 11:55 AM OneNote Examining samples Numerically Tuesday, January 28, 2025 9:32 AM Examining samples: You have your data, now need to look at it- does it look ok? ○ Possible outliers, make initial comparisons among samples, what kinds of statistical analyses can be applied Produce statistics to summarize our data ○ Sample statistics are estimators of population parameters What if we visualize the data with a dot-plot ○ Clustered or evenly distributed? ○ Arranging frequency of each value is called frequency distribution Descriptive statistics: N=sample size (count of observations in your sample) Measures of central tendency (or location) ○ Where are your data situated on the scale ○ Mean (average)= sum of values/n ○ Median = variate with equal # variates above and below it ○ Mode= most common variate (for discrete data) Mean: Median (M, Md, or x): https://uvic-my.sharepoint.com/personal/lucybryden_uvic_ca/_layouts/15/Doc.aspx?sourcedoc={9faa0b91-e898-498c-a6e1-c5e15b84c2ef}&action=edit&wd=target… 1/5 2/12/25, 11:55 AM OneNote Why use Median instead of Mean? We have an asymmetrical distribution ○ Non-normal-½ values above, ½ below the median Extreme values Descriptive statistics: Mode (Mo) Most frequent value Looking at our frequency distribution of test scores Mode is not commonly used for continuous data Discrete data: ○ Mean and median are meaningless ○ Mode is useful Measures of dispersion: Continuous data: Measures od dispersion- tell us about shape of distribution ○ Rande, interquartile range- smallest to largest values across whole or part of distribution Standard deviation, variance, coefficient of variation- reference amount of variation in sample Range: Largest-smallest number https://uvic-my.sharepoint.com/personal/lucybryden_uvic_ca/_layouts/15/Doc.aspx?sourcedoc={9faa0b91-e898-498c-a6e1-c5e15b84c2ef}&action=edit&wd=target… 2/5 2/12/25, 11:55 AM OneNote Also underestimates population range- how likely is it that the sample contains largest and smallest values from population Interquartile Range Mini-range between 1st and 3rd quartiles ○ Focus on variation at the center of distribution (middle 50%) and excludes outliers ○ Quartile- divides data points into 4 equal parts ○ Q1, Q2, Q3= data point at each division Variance and Standard Deviation: Variance and standard deviation tell us about how clumped or dispersed the data are Variance(s2): Measures average deviations of variates from mean ○ But: negative and positive deviations would cancel out, therefore square deviations ○ The sample statistic is s^2, population parameter is sigma ○ Standard Deviations (s, sd, or SD): Problem with variance, units of mesurement are squared, not intuitive, so take square root of variance = standard deviation https://uvic-my.sharepoint.com/personal/lucybryden_uvic_ca/_layouts/15/Doc.aspx?sourcedoc={9faa0b91-e898-498c-a6e1-c5e15b84c2ef}&action=edit&wd=target… 3/5 2/12/25, 11:55 AM OneNote Coefficent of variation (CV): Sd and s^2 are influecned by size of mesure, so cannot compare small to large measurements CV adjusts sd as porportion of Y https://uvic-my.sharepoint.com/personal/lucybryden_uvic_ca/_layouts/15/Doc.aspx?sourcedoc={9faa0b91-e898-498c-a6e1-c5e15b84c2ef}&action=edit&wd=target… 4/5 2/12/25, 11:55 AM OneNote https://uvic-my.sharepoint.com/personal/lucybryden_uvic_ca/_layouts/15/Doc.aspx?sourcedoc={9faa0b91-e898-498c-a6e1-c5e15b84c2ef}&action=edit&wd=target… 5/5