PSYC2012 Descriptive Stats & Normal Distribution

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Last updated 1:05 PM on 6/12/26
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9 Terms

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Descriptive Stats

Methods of summarising/organising raw data which provide basic insight but no inferences

> Visualisation = box plots, frequency tables & histograms, bar charts, scatter plots, line graph

> Central Tendency & Spread

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Measures of Central Tendency

1. Mean Balance point of distribution (2 decimal places). More sensitive to extreme scores so can be misleading representation of data.

2. Median The score that divides distribution in two equal parts (no. scores + 1 / 2).

3. Mode Highest frequency

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Central Tendency & Skewness

- Mean is sensitive to extreme scores

- Mode & median are "robust"

- Skewness does not affect mode, median a bit, mean dragged furthest in direction of skew.

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Measures of Variability/Spread/Dispersion

Range, IQR, Variance, SD

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Range

> Calc R: Maximum - Minimum

> Calc IQR: Q3 - Q1 (median of top half - median of bottom half)

> Crude:

R Only sensitive to lowest/highest score

IQR Specifies spread of middle 50% but still only tells you about 75/25%

> Large range = large variability

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Normal Distribution

Symmetric (re central tendency), bell-shaped probability distribution where mean, median & mode share same value.

+- 1 SD = 68%

+- 2SD = 95%

+- 3SD = 99.7%

<p>Symmetric (re central tendency), bell-shaped probability distribution where mean, median &amp; mode share same value.</p><p>+- 1 SD = 68%</p><p>+- 2SD = 95%</p><p>+- 3SD = 99.7%</p>
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Variance (Population)

Measure of variability that describes an average distance of every score from the mean.

> Considers all values!

> Average squared deviation

Step 1: Find mean

Step 2: Find deviation scores

Step 3: Average deviation scores

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Standard Deviation

Measure of variability that describes an average distance of every score from the mean

> Considers all values!

> Square root of variance to obtain index of variability in original units

> Symbol = Sigma

<p>Measure of variability that describes an average distance of every score from the mean</p><p>&gt; Considers all values!</p><p>&gt; Square root of variance to obtain index of variability in original units</p><p>&gt; Symbol = Sigma</p>
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Z-Score

Standardised deviation score!

Calc: Deviation score / SD

NOTE: Z-score 0 = mean, +1,2,3 above average, -1,2,3 below average (SDs)

+ Strong index of relative standing: standardising = eval. data point regardless of the original distribution's mean or variance.

+ Allows comparison of different datasets with different scales (e.g. performance in Maths vs. Chem)

E.G. Z-scores useful bc misleading comparison occurs when raw scores use different units or when difficulty is unequal

<p>Standardised deviation score!</p><p>Calc: Deviation score / SD</p><p>NOTE: Z-score 0 = mean, +1,2,3 above average, -1,2,3 below average (SDs)</p><p>+ Strong index of relative standing: standardising = eval. data point regardless of the original distribution's mean or variance.</p><p>+ Allows comparison of different datasets with different scales (e.g. performance in Maths vs. Chem)</p><p>E.G. Z-scores useful bc misleading comparison occurs when raw scores use different units or when difficulty is unequal</p>