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Lecture 3

PSYB07 - Lecture 3 Notes.docx

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University of Toronto Scarborough
Dwayne Pare

PSYB07: Data Analysis in Psychology Lecture 3 - September 26 , 2012 Descriptive Statistics Describing Distributions Modality – refers to the number of peaks in a data set Mode: the most frequent term in the data set (the peak of the distribution)  Histogram – first indication of the data  Smoothing the data (drawing the line over bars) – gives a good indication of the distribution’s shape  Classic bell curve/ the normal distribution o Tail, body, tail o Generally a peak in the center and symmetrical sides o Proportionate clustering of the data  Unimodal – one peak or mode o Common / normal o Bell curve  Bimodal – two peaks or modes o Heights of peaks could the same or different  Multimodal – more than two peaks or modes o Appears messy o To be avoided o No pattern within the data  Amodal (uniform) distribution – no peaks or modes o All values have the same frequency Symmetry  An asymmetric distribution is skewed o The body of the data is shifted to one side o One of the tails is longer than the other o Extreme or moderate skewness o The direction of the skew is the direction that the tail is pointing  Positively skewed (towards right, or positive numbers)  Negatively skewed (towards left, or negative numbers) Kurtosis  Refers to data clustering o How pointy or flat the shape of the distribution point o Doesn’t affect measures central tendencies  But affects measures of spread or range  Mesokurtic – normal distribution  Leptokurtic – pointier than a normal distribution o Less variability (in comparison to normal distribution)  Platykurtic – flatter than a normal distribution o More variability (in comparison to normal distribution) Descriptive statistics  The first way to describe the data o Characteristics of samples and or population  2 main methods o Measures of central tendency  The best measure/most representative to describe the data:  Mean – average of all scores o The x value corresponding to the balance point of the distribution o Mean = sum of scores / number of scores o “x bar” = sample mean and “mew” = population mean o Not necessary to order the data to calculate mean o Extreme values – affects statistics o Large values in data will affect the mean  The mean is sensitive to extreme values  Known as outliers – which need to be removed  Median – the half point o The midpoint of the distribution o The x value corresponding to the midpoint o Half of scores fall above, and other half fall below th o 50 percentile o Magnitude of values is not taken into account when calculating the median  Is not affected by outliers/extreme scores – is only concerned with that middle value Meaning 50% of the scores fall below the median (1) Arrange terms in numerical order (2) Median location = (N+1)/2 (3) Median is the value at that location Median does not have to be an actual score (in the situation of an even number of scores) (1) Order data (2) Median location = (N+1)/2 = (the middle of the third and fourth term) (3) Value of location 3.5 is the average of values at locations 3 and 4  Add values at locations 3 and 4 then find its average  That score is the median, even if it is not a score in the data  Mode – the point of highest frequency o The most common score o The x value corresponding to the peak of the distribution o Also very sensitive to outliers/extreme scores o In a normal distribution most data points are located near the middle of the distribution  summarize your data with a single number representing the center  Stem/Leaf – no data points are lost / all terms are displayed and listed
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