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Chapter 13

Chapter 13. Understanding research results: statistical inference. Inferential statistics. Are necessary to give meaning to sample data Population data is harder to acquire

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Chapter 13

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  1. Chapter 13 Understanding research results: statistical inference

  2. Inferential statistics • Are necessary to give meaning to sample data • Population data is harder to acquire • Used to determine if we can make statements that the results reflect what would happen if we were to conduct the experiment repeatedly w/ multiple samples • Allow us to arrive at conclusions on the basis of sample data

  3. Null and research hypotheses • Null hypothesis -- H0 • the population means are equal • The observed difference is due to random error • The H0 is rejected when there is a very low probability that the obtained results could be due to random error. • The IV had no effect • Research hypothesis -- H1 • The population means are not equal • The IV had an effect on the DV • If we can determine the null hypothesis is false, we then accept the research hypothesis is true. • Statistical significance • A very low probability that the obtained results could be due to random error. • Results are due to the IV’s effect on the DV

  4. Probability and sampling distributions • Probability • The likelihood of the occurrence of some event or outcome • What is the likelihood this occurrence will differ in the population • Based on specific information • Sampling distributions • Based on the assumption that the null hypothesis is true • When it is highly unlikely the null hypothesis is true (0.05 or 5% chance), the researcher rejects the H0 and accepts the H1 • Sample size • Larger sample sizes are good • With more observations, the greater the likelihood of obtaining an accurate estimate of the true population value

  5. The t test • t test • Commonly used to test if 2 groups significantly differ from each other • Does the mean of one group significantly differ from the mean of another group? • = group difference / within group variability • Group difference – the difference between the obtained means • Within group variability – the amount of variability around the group mean • If the t value has a low probability (a value of 0.05 or less) of occurring, the H0 is rejected

  6. The t test • Degrees of freedom • df • = the total # of participants in the groups – the number of groups • The number of scores free to vary once the means are known • One tailed vs. two tailed tests • One tailed tests are used if the research hypothesis specified the direction of difference between the groups • H1 = Group 1 will be > than Group 2 • Two tailed tests are used if the research hypothesis did not specify a predicted direction of difference • H1 = Two groups will differ

  7. The F test • F test is a.k.a. the ANOVA (analysis of variance) • An extension of the t test • Asks if there is a significant difference between 3 or more groups • Used to evaluate the results of factorial designs • Used when two or more independent variables are used • A ratio of two types of variance • Systematic variance – the deviation of the group means from the mean score of all individuals in all groups • Between group variance • Error variance – the deviation of the individual scores in each group from their respective group means • Within group variance • The larger the F ratio, the more likely it is that the results are significant

  8. The F test • Calculating effect size • Effect size – the magnitude of the effect • Can be in terms of t test or standard deviation • Provides information on the size of the relationship between the variable studied • Confidence intervals • A 95% confidence interval indicates that we are 95% sure that the population value lies within the range • As the sample increases the confidence interval narrows • This occurs because larger sample sizes are more likely to reflect the population mean

  9. Type I and II errors • Correct decisions • Rejecting the null hypothesis and the research hypothesis is true • Accept the null hypothesis and the null hypothesis is true • Type I error • Rejecting the null hypothesis when the null hypothesis is true • False positive; false alarm • The probability of making a Type I error is deterined by the alpha level, α • Type II errors • Accepting the null hypothesis when the research hypothesis is true • False negative • The probability of a type II error is called β

  10. Choosing a significance level • Researchers use a .05 or .01 significance level • Generally researchers think the consequences of making a Type I error are more serious than a Type II error • Interpreting non-significant results • Even though significance is not reached does not mean there is no relationship between the variables • Statistical significance does not always mean practical significance • To troubleshoot, modify the dependent measure for better reliability and sensitivity • If there are small sample sizes, it is harder to do statistical tests • Do multiple studies to ensure reliability

  11. Analysis • Choosing a sample size: power analysis • Power: the probability of correctly rejecting the null hypothesis • Power = 1 – p (Type II error) • A power between .70 and .90 is usually used • Usually done by a stats computer program • Significance of a Pearson R correlation coefficient • A statistical significance test allows you to decide whether to reject the null hypothesis and conclude that the correlation is greater than 0.0 • i.e. perform a t test to compare the obtained coefficient w/ the null hypothesis correlation (0.0) • Computer analysis of data • MS Excel, SPSS, SAS, Minitab…

  12. Selecting the appropriate significance test • One IV – 2 groups only • Nominal scale data • Chi square • Ordinal scale data • Independent groups: Mann Whitney U • Repeated measures or matched participants: Wilcoxon’s T or the sign test • Interval or ratio scale data • Independent groups: t test • Repeated measures or matched participants: t test or RM ANOVA • One IV – 3 or more groups • Nominal scale data • Chi square

  13. Selecting the appropriate significance test • One IV – 3 or more groups • Ordinal scale data • Independent groups: Kruskal – Wallace H test • Repeated measures: Friedman T test • Interval or ratio scale data • 1 way ANOVA • Two or more IVs • Nominal scale data • Chi square • Ordinal scale data • No appropriate test available • Interval or ratio scale data • 2 way ANOVA

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