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Lesson 6: Statistics OBJECTIVES* Deﬁne descriptive statistics * Deﬁne inferential statistics * Describe the types of statistics in Psychology:- calculate measures of central tendency including mean,median and mode-interpret p-values and draw conclusions based on, reliabilityincluding internal consistency; validity including construct andexternal-evaluate research in terms of generalizing the ﬁndings tothe population Friday, 6 April 2012
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Why research? The sole purpose for research is to be able to generalise results to the population. We research areas for two types of results: cause & effect, and correlations. Cause and effect studies aim to ﬁnd what causes something e.g. smoking causes lung cancer Correlational studies aim to ﬁnd relationships between two factors, e.g. as the population of smokers increases so to does the diagnosis of lung cancer. It is much easier to determine correlational results than causative.Friday, 6 April 2012
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Generalising Results To be able to generalise results, the following criteria must be met: The results show statistical signiﬁcance (p<0.05) All sampling procedures were appropriate All experimental procedures were appropriate All measures were valid All possible confounding variables were controlled.Friday, 6 April 2012
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Types of Statistics In psychology there are two types of statistics 1) Descriptive Statistics, show results 2) Inferential Statistics, explains results in relation to hypotheses.Friday, 6 April 2012
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Descriptive Statistics Includes the following: 1) Organising raw data into clear tables 2) Representing the data in graphs 3) Measures of Central Tendency 4) Measures of VariabilityFriday, 6 April 2012
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1)Organising Raw Data Frequency tables are the most common form of organising raw data. For example, Julie rolled a die 80 times and recorded the number shown on each throw: 1, 3, 6, 5, 2, 1, 6, 1, 5, 2, 1, 2, 5, 4, 3, 6, 5, 2, 3, 4, 1, 4, 3, 2, 5, 1, 6, 2, 3, 1, 5, 5, 2, 3, 5, 4, 1, 3, 5, 3, 6, 3, 1, 6, 6, 3, 3, 4, 3, 3, 6, 3, 1, 3, 4, 6, 2, 4, 6, 3, 4, 5, 4, 6, 2, 3, 4, 5, 5, 4, 2, 1, 5, 4, 5, 6, 1, 6, 2, 5. - This is raw data. To organise the data, a frequency table can be used. Here the amount of times the number was rolled (frequency) is listed beside the dice number. In frequency tables we also include the percentage of that frequency.Friday, 6 April 2012
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Calculating the percentage Number of times score occurs DIVIDED BY Total number of scores in data set MULTIPLIED BY 100 E.G. The percentage of rolling a 6 would be: 13/80 = 0.1625 x 100 = 16.25%Friday, 6 April 2012
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2) Representing the data Histogram Frequency Polygon Pie ChartFriday, 6 April 2012
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The normal distribution “Bell Curve” When one variable is continuous (meaning that it can have any value within a certain range) such as age in months or IQ, we can express the data as a line graph. For example, a teacher sets a group classwork activity and wants to ﬁnd out the group size that is most efﬁcient.Friday, 6 April 2012
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When data is presented in a line graph, psychologists hope that it forms a normal curve. This enables statistical procedures to be applied without further manipulation of the data.Friday, 6 April 2012
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3) Measures of Central Tendency (Measures in the Bell Curve) Tells us how the data are clustered near the central point of the dataset. There are three measures of central tendency 1) Mean - average of all the scores (calculated by adding up all the scores and dividing that total by the number of scores) 2) Median - the score that occurs exactly halfway between the lowest and the highest score. 3) Mode - the most commonly occurring score in the dataset.Friday, 6 April 2012
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4) Measures of Variability Opposite to measures of central tendency, measures of variability tell us about how scores are spread out. Three measures are used in measuring variability. 1) Range: Difference between the highest score and lowest score, E.G. 130 - 88 = 42 2) Variance: Provides a measure of how much, on average, each score differs from the mean. 3) Standard Deviation: Representation of the variance.Friday, 6 April 2012
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Calculating Variance and Standard Deviation Because some scores are higher and others are lower than the mean, if we were to simply average the differences , the negatives and positives would even out leading to an incorrect calculation. To overcome this, we square the differences, so that all ﬁgures are positive. (Remember two negatives equal a positive!) Mean: 110 The mean variance can be calculated by adding A score of 88: all the variances 110-88 = 22 so a together and dividing by score of 88 is 22 the total number of below the mean scores. therefore -22 484+256+121+64+25+1+1+1+81+22 5+225+400 A score of 119: DIVIDED BY 119-110 = 9 so a 12 EQUALS score of 119 is 19 157 over the mean therefore +9 So the mean variance is 157.Friday, 6 April 2012
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Standard Deviation Because the variance is a squared number, it makes it difﬁcult to compare results. This is why we use standard deviation (SD). The standard deviation puts the variance into a form that is useful in data analyse. To calculate the SD you take the square root of the mean variance. E.G. Square root of 157 = 12.5 Only get the SD for the mean variance! All the other variances still along the normal curve as SD from the mean.Friday, 6 April 2012
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Inferential Statistics Inferential Statistics are used once the descriptive statistics have identiﬁed there is a difference (variation) from the mean. What next is to determine if this difference or variance is signiﬁcant, or is it just due to chance. Inferential tests give a probability that the difference is caused by chance. This is expressed as a p value. Generally the lower the p value the better, however p<0.05 (that is 5 times in 100 or 5% of the time it is due to chance) is widely accepted.Friday, 6 April 2012
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p = 0.03 means there are 3 chances in 100 (3%) that this difference would be achieved by chance alone. If the level of signiﬁcance is p<0.05 then theseresults can be said to be statistically signiﬁcant as it is less then (<) 0.05 If the p value = 0.3 then the results are not signiﬁcant as 0.3 is greater then 0.05.Friday, 6 April 2012
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Complete ‘INVESTIGATE 1.6’ p 24 of textbookFriday, 6 April 2012
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Measures of relationship Correlational studies intend to establish the strength and direction of any relationship between two variables. Correlation: A statistical measure of how much two variables are related. Positive Correlation: Where the two variables change in the same direction. As one increases so to does the other. Negative Correlation: Where the two variables change in the opposite direction. As one increases the other decreases.Friday, 6 April 2012
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Strength in correlation The strength of a correlation can be calculated using the correlation coefﬁcient (r). The (+) or (-) sign before the coefﬁcient indicates if it is a positive or negative correlation. The number is the coefﬁcient, the higher the number the stronger the relationship.Friday, 6 April 2012
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Determine the strength (strong or weak) and direction (positive or negative) of the following correlations: r=- 0.74 r=+ 1.00 r=+ 0.23 r=- 0.15Friday, 6 April 2012
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