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An overview of descriptive and inferential statistics, focusing on the difference in mean ratings between men and women. It explains the concept of relative frequency, true difference, and random sampling error, and introduces the logic of statistical testing through null hypothesis significance testing (nhst).

Typology: Slides

2012/2013

1 / 24

Download Understanding Gender Differences: Introduction to Descriptive & Inferential Statistics and more Slides Statistics in PDF only on Docsity! Practicals, Methodology and Statistics Introduction 1 Docsity.com Descriptive Statistics Men’s mean rating Women’s mean rating 7.4 (SD = 1.3) 3.3 (SD = 1.5) 2 Docsity.com Inferential Statistics • No! There are two possible explanations for this difference • True difference – The difference in the samples represents a true or real difference in the populations • Random Sampling Error – The difference in the samples does not reflect a true difference but is due to random sampling error or variation 5 Docsity.com 6 Re la tiv e fr eq ue nc y µ 5 3 7 Random Sampling Error: Variability of a statistic from sample to sample due to chance Docsity.com 7 Re la tiv e fr eq ue nc y Both Females and Males means are estimates of the same population value Re la tiv e fr eq ue nc y Females Mean µ Males Mean µ µ Females and Males means are estimates of the means of different populations Ho Ha 3 3 7 7 Docsity.com Steps of NHST 4. Run the appropriate statistical test 5. Obtain the test statistic and associated p-value The probability of obtaining these results (i.e. test statistic) if the null hypothesis is true 6. Decide whether to reject or fail to reject Ho on the basis of the p-value 10 Docsity.com Decision Making • P-value – 0 – 1 – Conditional Probability – The probability of obtaining these results if Ho were true • If p-value is small… – It is highly unlikely that we would obtain these results if the Ho were true, so we can reject Ho in favour of Halt • If p-value is large… – It is very likely that we would obtain these results if Ho were true, so we cannot reject Ho 11 Docsity.com Decision Making • But what is large and what is small? • Convention • Significance Level / Rejection Level • P < .05 – Reject Ho if there is less than a 5% or less than a 1 in 20 chance of obtaining these results if Ho were true 12 Docsity.com SPSS Analysis • This value indicates the probability of getting this t statistic if the null hypothesis is true • We reject the null hyp if this value is less than 0.05 15 Independent Samples Test .209 .653 6.622 18 .000 4.1000 .61914 2.79924 6.622 17.522 .000 4.1000 .61914 2.79669 Equal variances assumed Equal variances not assumed SCORE F Sig. Levene's Test for Equality of Variances t df Sig. (2-tailed) Mean Difference Std. Error Difference Lower 95% Con Interval Differe t-test for Equality of Means Docsity.com P- values • For many researchers, attaining the “sig” p-value = Holy Grail • Joy at p =0.049 v Despair at p = 0.051 – Difference between the values = .002 • Beware: implications of NHST is that there can always be a simple “yes” or “no” answer as a result of study • Statistical significance does not equal clinical/practical significance or importance – Sufficiently large sample size will result in a statistically significant result 16 Docsity.com Logic of approach? • Something seems odd about this approach….. – Testing a hypothesis that is opposite to the one you wish to test • Falsification – Fisher – It is difficult to prove a statement but you can disprove it • “All dogs have one tail” • Can’t be sure even after viewing 10,000 dogs with one tail • But view one dog with two tails… • Provides a useful starting point for statistical tests 17 Docsity.com 20 Sampling distribution for a population of scores on an anxiety questionnaire for normal young people (mean = 50) Data on same questionnaire for young students (mean = 60) Qu: Do students’ levels of anxiety differ significantly from levels of young people in general? Qu: How likely is it that this sample of students came from this population? Ans: Calculate the % of samples with mean of 60 or more If % is very small (<5%), conclude that it is unlikely that this sample came from this population, This sample of students shows significantly higher anxiety levels than normal participants Docsity.com Sampling Distribution of a Test Statistic • Sample statistics – mean, median, variance, etc. • Test statistics – Results of statistical procedures – t, F, chi-square, etc. • All have their own sampling distributions – Can be used just like the sampling distribution of the mean 21 Docsity.com Let’s take the T Distribution • Recall earlier T-test – Investigate if there was a statistically significant difference between two groups – Calculated t for the two groups • T represented the difference between the two means • (Observed difference / standard error of the difference) – P-value • Probability of obtaining a t statistic this size if Ho was true • In the background… – P-value was calculated by comparing our computed t statistic with the sampling distribution for t when Ho is true 22 Docsity.com