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Stats !.pdf

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Stats !.pdf

  1. 1. Stats !☺
  2. 2. Types of data • Quantitative data: numerical data e.g. reaction times, height, any data set using only numbers • Strengths = easy to analyse, can create graphs and calculate averages from it, can eyeball data and see patterns at a glance • Weaknesses = oversimplifies behaviour, e.g. using scales to express feelings, means that individual meanings are lost • Qualitative data: non-numerical data, expressed in words e.g. transcribing an interview, extracts • Strengths = represents complexities, more detailed, can include information that is unexpected • Weaknesses = less easy to analyse, large amount of detail is difficult to summarise, difficult to draw conclusions- may be many ifs and buts • Primary data: collected first hand for research purpose, strength = specific to study, extracts only data you need, weaknesses= lots of time and planning, secondary data access takes minutes • Secondary data: collected by someone other than the person who is conducting the research, taken from journals articles etc., strengths = inexpensive and minimal effort, weaknesses = quality may be poor, information may be outdated or incomplete • Meta-analysis: secondary data that combines data from a large number of studies to calculate effect size, strengths = increases validity of conclusions, sample size is larger than the original samples, (as it is the sum), increases generalizability, weaknesses = publication bias, researchers may only select studies that follow their hypothesis leaving out other relevant but non-significant research, data may be biased itself
  3. 3. Types of data • Nominal (categorical): named data, separates into discrete categories, for example sex = male or female, or eye colour / hair colour • Ordinal: data that is placed into an order or rank, for example in a race finishing 1st,2nd,3rd , there is no standardised difference in time between scores – time between 2nd and 3rd has no need to be the same as between 1st and 2nd • Interval: numerical value data where the difference between points is standardised and meaningful, for example difference between 10 degrees temp and 20 degrees temp is the same as 20 to 30 degrees • Ratio: similar to interval data, standardised and meaningful difference between values, yet data must have a true zero = meaning you cannot have negative number in this data, an example would be height • Discrete data: numeric data, variables are finite, easily counted, non- negative for example number of students in a class, whole, concrete, fixed • Continuous data: can have any value, height, weight, temperature, lengths, can change over time in some situations (weight), complex, varying
  4. 4. Measures of data Measures of central tendency: • Mean: average, add all scores then divide by N • Median: middle value, place scores in ascending order then select middle value, (if 2 values calc. mean) • Mode: most frequent or common value, (used with nominal/categorical data Measures of dispersion: • Range: difference between highest to lowest value (+1) • Standard deviation: measure of the average spread around the mean, larger SD = more spread out the data is
  5. 5. Displaying quantitative data • Tables: raw scores in columns and rows, paragraph underneath to explain the data • Bar chart: categories (discrete data) usually placed a long the X axis, (bottom), frequency along the Y axis, (the side), this can be reversed • Histogram: bars touch each other, data is continuous rather than discrete, there is a true zero • Line graph: frequency on one axis, data on the other axis is continuous, line often depicts how something changes for example over time • Scattergram: used for correlational analysis, each dot represents one pair of related data, data on both axis must be continuous
  6. 6. Correlations The analysis of a relationship between variables, different to an experiment which analyses the measured change in DV from the manipulated IV, this looks at a comparison of two variable data sets or co- variables. They allow for researchers to investigate a relationship before conducting an experiment, or enable studies into sensitive areas where manipulating an IV would be inappropriate, however they cannot show the direction of which variable is causing the change in the other, meaning experimental analysis may be needed after, may be a third extraneous variable that is causing the relationship. • Positive correlation: data rises and falls together • Negative correlation: one co-variable rises as the other falls • No correlation: no pattern in the data set
  7. 7. Distributions • Shows the frequency of data. Normal distribution should be in a symmetrical bell shaped curve, most people in the middle (average), with few at either end of the extremes, the mean, median and mode occupy the same mid-point of the curve • Skewed distributions lean to one side or the other because most people are at either the lower or upper end • Mean media and mode will always appear for each type as shown here ->
  8. 8. Inferential statistics / statistical testing Significance: the difference or association between two sets of data is greater than what would occur by chance, (fluke), to find out if the difference is significant we need to conduct stats tests Probability: known as ‘p’, numerical measure of the likelihood that certain events will occur, in psychology we use 0.05 for p which is the same as 5%, so this means that if the change or difference is seen as significant, there is a less than 5% probability that the results occurred by chance. We accept a p result of 0.05 or below as significant. - The outcome of the statistical test is the calculated value - This can then be compared to a critical value, (found in critical values tables), if it is the same or less than the critical value, the calc. value is seen as significant! - To compare to a critical value, you need to know the significance level / p (usually will always be 0.05),, the number of the participants in the investigation (N), or the degrees of freedom (df = N-1), and whether the hypothesis is directional, (a stated prediction of positive or negative changes), or non directional (no known direction, just suggested there is a correlation or association) -
  9. 9. The Sign test! • Used to analyse the difference in scores between related items, for example the same participant is tested twice = repeated measures or matched pairs • Used with nominal data Calculation: 1. Score for condition B is subtracted from condition A, to produce the sign of the difference = either a + or – 2. Total number of pluses and total number of minuses calculated 3. Participants who achieved the same score in conditions A and B should be disregarded AND deducted from the N value 4. The S value is the total of the less frequent sign 5. Then compare this calculated S to the table of critical values, if S is less than or equal to CV, the experimental hypothesis H1 is retained, otherwise it is rejected
  10. 10. Example question • Is there a significant improvement in the scores at 5% significance level?

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