N211 Class 2 PDF

N211 Class 2 Office Hours Poll https://forms.gle/xdsh6pSGDFTxPYf1A INTRODUCTION Quick Review of Last Week Descriptive Statistics ○ Mean, median and mode ○ Introducing:Normal distribution Histograms LEVELS OF MEASUREMENT Level of Measurement Central Tendency Graphs Nominal...

N211 Class 2 Office Hours Poll https://forms.gle/xdsh6pSGDFTxPYf1A INTRODUCTION Quick Review of Last Week Descriptive Statistics ○ Mean, median and mode ○ Introducing:Normal distribution Histograms LEVELS OF MEASUREMENT Level of Measurement Central Tendency Graphs Nominal Mode Bar, Pie Ordinal Mode, Median Bar, Pie Interval Mean, mode, median Bar, pie, Box plot, histogram, Ratio Mean, mode, median Histogram, box plot Examples Related to Nursing Nominal: Blood types (A, B, AB, O) Ordinal: Pain scales (0 = No Pain…….. 10 Worst Pain Ever) Interval: Core temperature measured in Degrees Celsius Ration: Patient’s weight in Kg DESCRIPTIVE STATISTICS Descriptive statistics = Presentation, organization and summarization of data ○ Graphical representation & Tables Typically the first thing a health researcher do: ◦ Includes demographic data e.g. age, smoking, comorbidities, education etc SUMMARY STATISTICS: MEASURES OF CENTRAL TENDENCY Given a data set, a measure of the central tendency is a value about which the observations tend to cluster. OR It is a value around which a data set is centered. CENTRAL TENDENCY Three main measures: 1. Mean (Average) 2. Median 3. Mode MEAN Mean: The average score o Used for variables measured at the interval and ratio level o Calculate by adding up the numbers in a distribution and then divide by the number of observations EXAMPLE OF MEAN Sample Mean: Age of the patients coming to the clinic 57,86,42,38,90,66 EXAMPLE 1: CALCULATE THE MEAN Study Participant Annual Household Income 1 $10,000 2 $45,000 3 $54,000 Mean = sum of all items divided by 4 $62,500 number of items 5 $57,500 In this case, mean = $49,143 6 $68,000 7 $47,000 Discussion Questions 1. How might small samples impact on the mean? 2. How might large samples impact on the mean? 3. How might outliers affect the mean? MEDIAN o Median: The middle value in an ordered array o Used for variables measured at the ordinal, interval or ratio level o Calculating the Median Steps: 1) List the values from lowest to highest 2) Find the middle score (n+1/2) 3) For even number of numbers, take the average of two MEDIAN: EXAMPLE Age of the patients coming to the clinic 3, 4, 5, 7, 8, 9, 11, 14, 15, 16, 16, 17, 19, 19, 20, 21, 22 1. Need to Order the data There are 17 terms in the ordered array above. Position of median = (n+1)/2 = (17+1)/2 = 9 o The median is the 9th term 15. MODE Mode: The most frequent category o Used for variables measured at the nominal level, ordinal, interval and ratio o Can have more than one mode Example: List of blood types available in blood bank O+ve, B+ve, A+ve, AB-ve, O-ve, B-ve, O+ve, A+ve, O+ve, O-ve the mode is equal to O+ve. Examples of How Central Tendency Used in Nursing ◦ Average medication dose based on patient's height and weight ◦ Average patient satisfaction scores ◦ Median age of patients in a nursing home ◦ Mean blood pressure readings of a group of patients to assess the overall cardiovascular health of the group. Plotting Frequencies - Histograms Display of the frequencies Visual representation of the data Useful for large data sets Shape depends on the data Plotting Frequencies - Histograms What is this shape called? And these? MODE, MEAN AND MEDIAN https://medium.com/@statscafe123/measures-of-central-tendency-b9cebaaeccad frequent here Mode Mean Mode Median  No Mode all equal here so no mode Mean Median Kurtosis more and more focus, bigger sample small distirbution,, most likely outliers When should I report which measures? Report Mode when dealing with frequency distributions for nominal data. Range is often reported because it orients readers to the nature of the sample. Measures for Skew and Kurtosis are seldom reported. For extreme shapes, boxplots or histograms are generally preferred. Questions and Break MEASURES OF VARIABILITY/ SPREAD/ DISPERSION Measures of variability describe the spread or the dispersion of a set of data. Common Measures of Variability o Range o Variance o Standard Deviation  Some Examples for Nurses Variations in Physical Vital signs and lab results Variability in patients' Variations in care processes assessment : Help to identify Variability: help nurses admissions: understanding and outcomes: Helps in risk assessment and help understand the range of the variability in patient quality improvement nurses and healthcare teams values for different patients, admissions helps hospitals initiatives. assess the risk of allowing them to tailor allocate staff and beds complications and make interventions and care plans effectively. timely interventions. accordingly.  * THE RANGE ◦ How far apart scores are from the mean 35 41 44 45 How do I calculate it? 37 41 44 46 ◦ Range = highest value – smallest value 37 43 44 46 ◦ Usually smallest and largest values reported 39 43 44 46 ◦ Example: if highest value is 48 and smallest value is 35 the range could be reported as 40 43 44 46 ◦ 13 OR 40 43 45 48 ◦ 35-48  VARIANCE AND STANDARD DEVIATION Variance: = Average of the Squared (WHY???) values around the mean Measures how spread out the data is Average distance of the values from the arithmetic mean It is the measure of how spread out the values are around the mean. Small variance = most scores close to the average Large variance = scores are widely spread Standard Deviation: = square root the variance (see above). Gives info on the amount of variation Tells you how far the responses/ numbers are spread from the mean.  Variance – (around mean) Mean = 8 find out the variation Variance and Standard Deviation Both give information about the distribution of your data Variance changes the unit to squared……… ○ Mean height 170cm ○ Data points 150cm 160cm 170cm 180cm 190cm ○ Variance ○ (150-170)2 = 400 ○ (160-170)2 = 100 ○ (170-170)2 = 0 ○ (180-170)2 = 100 ○ (190-170)2 = 400 ○ Variance = (400+100+0+100+400)/ 5 ○ So variance = 200cm2 Variance and Standard Deviation Both give information about the distribution of your data ○ Mean height 170cm ○ Data points 150cm 160cm 170cm 180cm 190cm Calculating the SD returns the measure to the original unit Here SD=Square root of 200 SD =14.14 cm As the standard deviation is in the same unit as the original data, it’s much easier to understand what the number represents. FORMULA FOR CALCULATING THE VARIANCE AND STANDARD DEVIATION  Other measures of variability; Inter-Quartile Range Can divide the distribution into Quarters Recall that the Median is ‘the middle value/point of a set of ordered numbers below which 50% of the distribution falls’ The Median is also the ‘50th percentile’; the point below which 50 per cent of the ordered values in the distribution fall. Inter-Quartile Range (IQR) Measures (Interquartile Range [IQR]) The IQR is a measure of variability that is natural to use if you are going to be using the Median as a measure of central tendency. Interquartile Range (IQR): range of values extending from 25-75% ○ It is the range of the middle 50% of the distribution Like the median, IQR is not sensitive to extreme scores Example from Public Health 97th percentile 85th percentile 50th percentile 15th percentile 3rd percentile 97th percentile 85th percentile 50th percentile 15th percentile 3rd percentile Visual Representation of IQR When should I report which measures? Report Mean for central tendency and Standard Deviation for variability when a distribution is reasonably symmetrical, with few extreme scores, and one mode. Report Median for central tendency and Inter-Quartile Range for variability with nonsymmetrical distributions because it is not sensitive to skewness (but report the mean and standard deviation as well). When should I report which measures? Report Mean for central tendency and Standard Deviation for variability when a distribution is reasonably symmetrical, with few extreme scores, and one mode. Report Median for central tendency and Inter-Quartile Range for variability with nonsymmetrical distributions because it is not sensitive to skewness (but report the mean and standard deviation as well). Inferential Statistics DEFINITION Inferential statistics is a branch of statistics that allows us to make predictions or inferences about a larger population based on a sample of data taken from that population. It involves using the data to estimate, test hypotheses, and make predictions.  * Inferential Statistics A way of checking our sample different from larger population Sample Population ….all children age 5-9 in Canada Sample: 45 children Population from ….all Edmonton children age who are 5-9 5-9 in years of age Alberta  INTRODUCTION TO INFERENTIAL STATISTICS Key concepts that underpin inferential statistics 1. Probability 2. Normal distribution 3. Population and sample 4. Standard scores (z-scores) Types and Assumptions Two types: Parametric and Non-parametric statistics Parametric statistics assumptions ○ Random sample ○ Unbiased selection ○ Normal distribution of variable in the population ○ Observations are independent of each other ○ Homogeneity of variance Use non-parametric when any of the above assumptions not met or unsure! Inferential Statistics - MoreNext Week! Can infer a point estimate (single value) Can infer range of values = confidence intervals Population and sample ○ How might these be different? Selecting the sample ○ Why might this be important? Testing a hypothesis (an idea) ○ Testing whether it fits the data collected Error ○ Error will always occur ○ Maybe different types of error ○ Error might be down to data collection, data interpretation, sample Reminders One-min paper today Office hour poll Stats prep #2 Next week = Quiz 1 51