Tuesday, April 8 n Inferential statistics – Part 2 n Hypothesis testing n Statistical significance n continued….

n What you want to know is what is going on in the population? n All you have is sample data n Your research hypothesis states there is a difference between groups n Null hypothesis states there is NO difference between groups n Even though your sample data show some difference between groups, there is a chance that there is no difference in population

SamplePopulation ? Male GPA= 3.3 Female GPA = 3.6 Inferential N=100 Parameter Ha: Female students have higher GPA than Male students at UH

Three Possibilities n Females really have higher GPA than Males n Females with higher GPA are disproportionately selected because of sampling bias n Females’ GPA happened to be higher in this particular sample due to random sampling error Male GPA= 3.3 Female GPA =3.6

Logic of Hypothesis Testing Statistical tests used in hypothesis testing deal with the probability of a particular event occurring by chance. Is the result common or a rare occurrence if only chance is operating? A score (or result of a statistical test) is “Significant” if score is unlikely to occur on basis of chance alone.

The “Level of Significance” is a cutoff point for determining significantly rare or unusual scores. Scores outside the middle 95% of a distribution are considered “Rare” when we adopt the standard “5% Level of Significance” This level of significance can be written as: p =.05 Level of Significance

P <.05 Reject Null Hypothesis (H 0 ) Support Your Hypothesis (H a )

Decision Rules Reject H o (accept H a ) when sample statistic is statistically significant at chosen p level, otherwise accept H o (reject H a ). Possible errors: You reject Null Hypothesis when in fact it is true, Type I Error, or Error of Rashness. B.You accept Null Hypothesis when in fact it is false, Type II Error, or Error of Caution.

Correct H o (no fire) H a (fire) H o = null hypothesis = there is NO fire H a = alternative hyp. = there IS a FIRE Accept H o (no fire) Type II error Type I error Reject H o (alarm) True State

What Statistics CANNOT do n Statistics CANNOT THINK or reason. It’s only you who can think. n Something can be statistically significant, yet be meaningless. n Statistics - about probability, thus canNOT prove your argument. Only support it. n Reject null hypothesis if probability is <.05 (probability of Type I error < than.05) n Statistics can NOT show causality; can show co-occurrence, which only implies causality.

When to use various statistics n Parametric n Interval or ratio data n Non-parametric n Use with non- interval/ratio data (i.e., ordinal and nominal)

Parametric Tests n Used with data w/ mean score or standard deviation. n t-test, ANOVA and Pearson’s Correlation r. n n Use a t-test to compare mean differences between two groups (e.g., male/female and married/single). n

Parametric Tests n use ANalysis Of VAriance (ANOVA) to compare more than two groups (such as age and family income) to get probability scores for the overall group differences. n Use a Post Hoc Tests to identify which subgroups differ significantly from each other.

When comparing two groups on MEAN SCORES use the t-test.

When comparing more than two groups on MEAN SCORES, use Analysis of Variance (ANOVA) The computer will do all the work!

T-test n If p<.05, we conclude that two groups are drawn from populations with different distribution (reject H 0 ) at 95% confidence level

Is there a meaningful difference between subgroups? Question: Answer : Use Inferential Statistics to help you decide if differences could be due to chance, or are they likely a true difference between groups. If differences are too large to be due to chance, then there is a Significant Difference between the groups. We know the probability that our conclusions may be incorrect.

Males: Mean = 11.3 SD = 2.8 n = 135 Females: Mean = 12.6 SD = 3.4 n = 165 Mean scores reflect real difference between genders. Mean scores are just chance differences from a single distribution. ** Accept Ha Accept Ho p =.02

Married: Mean = 11.9 SD = 3.8 n = 96 Single: Mean = 12.1 SD = 4.3 n = 204 Mean scores reflect real difference between groups. Mean scores are just chance differences from a single distribution. Accept Ha **Accept Ho p =.91

Decision Making 2 ways you can be “right” Your inference based on sample data: Reject H 0 Accept H 0 Reality H 0 trueH 0 false

Decision Making 2 ways you can be wrong X Type II error X Type I error Your inference based on sample data: Reject H 0 Accept H 0 Reality H 0 trueH 0 false

Correlation - Measures of Association n Pearson’s Correlation Coefficient both variables interval / ratio data one variable interval and other nominal one variable interval and other nominalNon-parametric: n Spearman’s Rank Order Correlation with ordinal data n Phi coefficient Both variables are dichotomous (2 choices only)

Measures of Association n Measures of association examines the relationship between two variables = bivariate analysis n Measures of association involves the significance test n Significance test examines the probability of TYPE I error n Conventionally we reject the null hypothesis if probability is <.05 (probability of TYPE I error is smaller than.05)

Measures of Association OrdinalIntervl/Ratio Nominal Ordinal Intervl/Ratio Correlation (Spearman) Correlation (Pearson)  Measures of association to use depends on which level your variables are measured Nominal Phi coefficient

When selecting a potential dating partner, how important are the following characteristics?