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Significance and probability Type I and II errors Practical Psychology 1 Week 10

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2 Descriptive Statistics: a review Describe numerical data Communicate numerical findings in standardized (means, sd, N in the form of a table) & pictorial ways (bar chart) Techniques for describing data: Figures (bar chart, pie chart, S&L plot, etc.) Measures of central tendency and dispersion (Mean, median, SD, range, etc.) RF, percentiles Distributions (Z-scores and SND curve Next week)

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3 E.g. Descriptive statistics table and figure

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4 Inferential Statistics Inferential statistics is based upon probability Used to make inferences about whether the characteristics of a sample is a good representation of characteristics of the population. Allow inferences to be made from the numerical findings. Permit different kinds of conclusions to be reached (e.g. significant difference in driving ability between males and females)

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5 What is probability? Probability (p) describes random or chance events; refers to how likely a particular outcome is. Event must be random, so outcome be determined by luck. E.g. coin: p (getting Heads) = 1 in 2 or 0.5 or 50% Probability can be expressed as a ratio, fraction, or percentage. Probability of events occurring is measured on a scale from 0 (not possible)________________ to 1 (must happen).

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6 Hypotheses… review Usually stated in terms of the dependent (DV) and independent variables (IV). Null Hypothesis Experimental Hypothesis one-tailed (directional) two-tailed (non-directional) It is on the basis of inferential testing that a hypothesis can be accepted or rejected.

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7 Null hypothesis Ho a null hypothesis is a hypothesis set up to be falsified in order to support an alternative hypothesis ( the experimental).alternative hypothesis the null hypothesis is presumed true until statistical evidence in the form of a hypothesis test indicates otherwise.evidence a null hypothesis is often the reverse of what the experimenter actually believes; it is put forward to allow the data to contradict it.

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8 Social scientists reject the null hypothesis H 0 (that differences occur at a chance level only), when the probability of this being true drops below 0.05 (5%)... ...this is often called alpha (α), the “5% significance level”. Significance level α (alpha)

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9 SPSS output

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10 Significance level 5% 5% (0.05) Conventional significance level. if the p-value is close to 5% it may well be decided that the research is worth pursuing. If a result is significant (p < 0.05 “less than 0.05”) the null hypothesis is rejected. If a result is not significant (p ≥ 0.05 “greater than or equal to 0.05”) the null hypothesis is retained/ not rejected. By 'result is significant' we mean 'the difference (or relationship) is unlikely to have occurred by chance at the set level'

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11 Significance levels 1% (0.01) Stricter, preferred for greater confidence than the conventional one If we are about to challenge a well-established theory or research finding by publishing results which contradict it, the convention is to achieve 1% significance before publication. When the researcher only has a one-off chance to demonstrate an effect (replication may be impossible in many field studies or “natural experiments”).

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12 Significant difference at 5% (p<0.05) “the difference is significant” “the correlation is significant” Significant at 1% (p<0.01) “the difference is HIGHLY significant” “the correlation is HIGHLY significant”

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13 Significance level 10% (0.1) Significance level generally considered too high for rejection of the null hypothesis, but which might merit further investigation. a researcher cannot be confident of results, or infer an actual effect, if the level achieved is only 10%.

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14 Type I and Type II errors If the null hypothesis is true, but has been rejected because p<0.05, it is said that Τype I error has occurred. A Τype II error occurs when the null hypothesis is retained, because p>0.05. Yet, there is a real underlying effect.

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15 Type I and Type II errors Type I error: Mistake made in rejecting the null hypothesis when it is true Type II error: Mistake made in retaining the null hypothesis when it is false.

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16 Type I and Type II errors Decision Null hypothesis H 0 is actually: AcceptedRejected True Type I error FalseType II error

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Stay tuned for… Independent samples T-test

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