Inferential statistics

Question 1

PARAMETRIC TESTS: THE NORMAL DISTRIBUTION

Answer 1

 Term “parametric” defined in 1942: “distribution functions of the variables…are assumed to be of known functional form”.
 A frequency histogram of the result obtained from repetitive measurements made of biological variables frequently follows a characteristic shape likened to that of an upside down bell.
 The normal distribution has some special characteristics.

Question 2

STUDENT’S T-TEST

Answer 2

The t‐test assesses whether the means of two groups are
statistically different from each other. This analysis is appropriate whenever you want to compare the means of two groups.

Question 3

T-TEST

Answer 3

• When the value on the top of the equation is large, or the value on the bottom of the equation is small, the overall ratio will be large.
• The larger the value of t, the more likely it will be significant.

Question 4

T-TEST EXAMPLE

Answer 4

 Question: Is there a relationship between father smoking status and “parental reaction score”, a measure of parents’ reactions to finding out if their child has been smoking.
 Seven items‐ e.g. ‘I would be very angry’, ‘ I would discuss it with my child’; Responses
‐ 1 definitely not' to 5 definitely yes‘; higher score =
more “constructive” reaction (some items were reversed)
 Father smoking is the independent variable and parental reaction score is the dependent variable.
 Two means (hypothetical data for 54 cases, 27 in each group)
 Father smokes‐no, M1=29.9 [SD=3.6] vs Father smokes‐yes, M2=27.7 [SD=4.2]

Question 5

UNMATCHED VS. MATCHED (PAIRED) T-TEST

Answer 5

 Some statistical tests are designed to assess groups that are unmatched or independent.
 Is the admission systolic blood pressure different between men and women?

 Some statistical tests are designed to assess groups that are matched or data that are paired.
 Is the systolic blood pressure different between
admission and discharge? I.e. same subjects before and after intervention.

Question 6

INTERACTION EFFECTS

Answer 6

 Study looking at relationship between two independent variables 1) level of exercise, 2) when exercise is taken and the dependent variable: hours of sleep at night.
 Interaction is indicated by non‐parallel lines in a line graph. In other words, if the lines are crossed then there is an interaction.
 Of course the lines are rarely perfectly parallel, so the real question is about whether the different pattern of means across the sub‐groups is to be considered unlikely to have occurred by chance.

Question 7

CORRELATION BETWEEN TWO INTERVAL VARIABLES (PARAMETRIC)

Answer 7

Pearson’s correlation reflects the degree of linear relationship between two variables. It ranges from +1 to ‐1. A correlation of +1 means that there is a perfect positive linear relationship between variables.