Download 922 exercise solution final

922 - Statistics exercise – Shira Farby
The exercise below has two parts.
Part I (sections B & C) should be submitted by 19/12/11
Part II (sections D-G) should be submitted by 9/1/12 (after a short intro to excel on
the 26/12)
Late submissions will NOT be accepted
A. Experiment description
A linguistic experiment tested 58 children who are Russian-Hebrew bilinguals
(speak Russian at home, and Hebrew at the preschool). In a background information
form the age of the children in months was marked, as well as how long they have
been exposed to Hebrew. Two questions in the background information form were to
what extent the child's mother uses Russian (more / less) and to what extent the child's
mother uses Hebrew (more/less). As theses are separate questions, both can be
answered as "more".
One part of the experiment was on social identity, and the children were asked to
rate (on a scale of 1 to 10) to what degree they agree with the following social labels:
Russian, Israeli, Ivri, Jewish.
The second part of the experiment was linguistic, and the children were asked to
repeat sentences in Hebrew and Russian. The score of two linguistic indicators from
the repeated sentences was computed separately (repeating prepositions correctly,
repeating plural inflection correctly).
Part I – for 19/12/11
B. Design
1. Name 3 independent variables. What is the type of their scale? (exhaustive list)
Variable
Scale
Age
Ratio
Length of exposure to Hebrew
Ratio
Mother in terms of Russian use
Nominal
Mother in terms of Hebrew use
Nominal
2. Name 3 dependent variables. What is the type of their scale? (exhaustive list)
Variable
Scale
How much do you agree Russian
Ordinal
How much do you agree Israeli
Ordinal
How much do you agree Ivri
Ordinal
How much do you agree Jewish
Ordinal
Repeating prepositions correctly- Hebrew
Ratio
Repeating plural inflection correctly- Hebrew
Ratio
Repeating prepositions correctly- Russian
Ratio
Repeating plural inflection correctly- Russian
Ratio
3. How many conditions are in the social part? Give them names.
Four conditions: Russian identity, Israeli identity, Ivri identity and Jewish identity.
4. How many conditions are in the linguistic part? Give them names.
There are four conditions, arranged in a 2x2 design. The conditions are (1) the
language tested (Russian/Hebrew) and (2) the linguistic part repeated (preposition /
plural inflection). The four conditions are: Preposition repetition in Hebrew,
Preposition repetition in Russian, Plural inflection repetition in Hebrew, Plural
inflection repetition in Russian.
C. Hypothesis
1. Choose one part of the experiment (social/linguistic), and phrase for it an
experimental hypothesis. Remember that the hypothesis predicts an effect of
independent variable(s) on dependent variable(s).
There are many possible experimental hypotheses; only two are given here as
examples. Please use your own hypothesis for part II.
Social
The more the mother uses Russian, the child will rate the social label “Israeli”
lower than “Russian”
Linguistic
The longer the time a child is exposed to Hebrew, s/he will score higher on the
Hebrew tasks (correct repetition of prepositions/plural inflection).
2. What is the null hypothesis for your hypothesis?
Social
The mother’s use of Russian (more/less) does not affect the child’s rating of the
social labels “Israeli” and “Russian”
Linguistic
The length of exposure to Hebrew does not affect the score of Hebrew tasks
(correct repetition of prepositions/plural inflection).
3. What is the direction of your hypothesis?
Social
The direction of this hypothesis is negative. In order to reject the null hypothesis,
the results for the social label “Israeli” will have to be at the lowest 5% of the
distribution of children whose mother uses more Russian.
Linguistic
The direction of this hypothesis is positive. In order to reject the null hypothesis,
the results of the Hebrew tasks (correct repetition of prepositions/plural inflections)
will have to be at the highest 5% of the distribution of children with long exposure
to Hebrew.
Part II – for 9/1/12
D. General computations
1. For the variable "age" compute the mean and median.
The mean of age is 69.67 months.
The median of age is 70 months.
2. For the variable "Length of exposure to Hebrew" compute the mean and standard
deviation.
The mean is 3.75 years.
The standard deviation is 1.37 years.
3. For the variable "Mother in terms of Russian use" compute the percent of "more"
responses.
The percent of “more” responses is 84.48%
4. For the variable "Mother in terms of Hebrew use" compute the ratio of "more"
responses.
The ratio between “more” and “less” responses is 39/19
5. For the variable "How much do you agree: Ivri" compute minimum, maximum and
range.
The minimum is: 1
The maximum is: 10
The range is 1 to 10.
6. For the variable "How much do you agree: Israeli" construct a frequency table.
Rating
1
2
3
4
5
6
7
8
9
10
Frequency
15
4
1
3
3
2
1
1
0
28
7. For the variable "preposition repetition, Hebrew" compute the proportion of correct
repetition (for each child), and add this as a new column to the excel table.
Proportion is written in real numbers, 28/30 and so on.
 Thinking question: what is the difference between the new column (proportion
of prep repetition) and the old grade (prep repetition)?
 Answer: instead of N correct responses, we have a grade (which can be
comparable to other grades).
8. For the variable "preposition repetition, Russian" construct a column with percent
of correct responses for each child, and fill in the following table:
% of correct
Frequency
cumulative frequency
percentile
40-70
6
6
10.34%
71-80
7
13
22.41%
81-90
6
19
32.76%
91-95
17
36
62.07%
96-100
22
58
100.00%
Total N
58
preposition
(Russian)
 Optional: generate a frequency graph for this variable.
E. Descriptive statistics
1. Social hypothesis
In a 2x2 design of 4 conditions, the effect of the mother's use of Russian
(more/less) as the independent variable on the social identity (Israeli/Russian) as
the dependent variable(s) was measured in a rating task, on a scale of 1-10. (N=58)
Linguistic Hypothesis
In a 2x2 design of 4 conditions, the effect of the length of the child's exposure to
Hebrew (more/less) as the independent variable on the correct repetition of Hebrew
functional categories (preposition/plural inflection) as the dependent variable(s)
was measured in a sentence repetition task. (N=58)
2. Construct the appropriate table to report mean and standard deviation of all
conditions.
Social label
Mother's
use Mean
Std
of Russian
Israeli
Russian
More
6.31
3.97
Less
5.67
4.39
More
6.73
3.79
Less
5.0
4.52
For the linguistic task, the variable "length of exposure" was used to divide the
children to two groups, based on its mean. The groups are: "less exposed"
(range:0.5-3.17, N=18) and "more exposed" (range:3.25-5.75, N=40). In
addition, the linguistic grades were computed as percents for the repetition
tasks.
Repetition,
Length
of mean
Std
Hebrew
exposure
Preposition
More
0.89
0.12
Less
0.89
0.086
Plural
More
0.86
0.12
inflection
Less
0.88
0.086
3. Optional: generate a histogram of the findings.
F. Initial Conclusions
1. Do the findings of this group suggest that your hypothesis is in the right direction?
Social: Looking at the "more" group, the mean for "Israeli" is slightly lower (6.31)
than the mean for Russian (6.73). Thus, the raw means support the hypothesis.
Linguistic: For both categories (preposition/plural inflection) the "more" group was
expected to have higher means than the "less" group. This is not supported. For
preposition repetition, both groups perform equally well (0.89); for plural
inflection, the "more" group actually performed slightly lower (0.86) than the
"less" group (0.88).
2. Do the findings support the effect of the independent variable(s)?
Social: The choice of "Mother's use of Russian" as the independent variable shows
an effect on social identity; for both labels (Israeli/Russian) the "less" group has
lower means (5.33) than the "more" group (6.52).
Linguistic: The choice of the mean of "length of exposure" (3.17) for dividing the
children into two groups (more/less) does not seem to have an effect on the
performance in these tasks.
G. Inferential statistics
1. Name the statistical test you will use to see if the effect is significant.
Social: there is one independent variable (one-way test), but two measures from
each child (repeated). The grades are ordinal, hence, a non-parametric test is
required: Friedman’s ANOVA (which is parallel to a one-way ANOVA).
Linguistic: there is one independent variable (one-way test), but two measures
from each child (repeated). The grades are computed as percents, and hence are on
a ratio scale. The test is a one-way repeated ANOVA.
2. How many degrees of freedom do you have?
In general, for a t-test we will have df = N-1 =57.
For ANOVA we have an F score, which requires us to compute df within groups,
as well as df between groups. For both hypotheses, df within = k-1=1, and df
between = N-2 = 56. (Since we have two groups we lose a degree of freedom for
each group).
3. How will you compute the critical value for rejecting the null hypothesis? ( or
/2).
Since both hypothesis have a direction the critical value will be computed using .