# Trends in International Mathematics and Science Study (TIMSS)

The Trends in International Mathematics and Science Study (TIMSS) tracks the math and science competency of fourth graders across about fifty nations.

A series of tables with one record per school (ACG), per student (ASG), per teacher (ATG), as well as files containing student achievement (ASA), home background (ASH), student-teacher linkage (AST), and within-country scoring reliability (ASR).

A complex sample survey designed to generalize to the fourth-grade student population of participating countries.

Released quadrennially since 1995.

Funded by the International Association for the Evaluation of Educational Achievement and compiled by the Lynch School of Education at Boston College.

## Simplified Download and Importation

The R `lodown`

package easily downloads and imports all available TIMSS microdata by simply specifying `"timss"`

with an `output_dir =`

parameter in the `lodown()`

function. Depending on your internet connection and computer processing speed, you might prefer to run this step overnight.

```
library(lodown)
lodown( "timss" , output_dir = file.path( path.expand( "~" ) , "TIMSS" ) )
```

`lodown`

also provides a catalog of available microdata extracts with the `get_catalog()`

function. After requesting the TIMSS catalog, you could pass a subsetted catalog through the `lodown()`

function in order to download and import specific extracts (rather than all available extracts).

```
library(lodown)
# examine all available TIMSS microdata files
timss_cat <-
get_catalog( "timss" ,
output_dir = file.path( path.expand( "~" ) , "TIMSS" ) )
# 2015 only
timss_cat <- subset( timss_cat , year == 2015 )
# download the microdata to your local computer
timss_cat <- lodown( "timss" , timss_cat )
```

## Analysis Examples with the `survey`

library

Construct a multiply-imputed, complex sample survey design:

```
library(survey)
library(mitools)
library(RSQLite)
# load the ASG (student background) + ASH (home background) merged design
timss_design <- readRDS( file.path( path.expand( "~" ) , "TIMSS" , "2015/asg_design.rds" ) )
design_weights <- readRDS( file.path( path.expand( "~" ) , "TIMSS" , "2015/asg_weights.rds" ) )
five_tablenames <- paste0( "asg_2015_" , 1:5 )
timss_design <- lodown:::svyMDBdesign( timss_design )
```

### Variable Recoding

Add new columns to the data set:

```
timss_design <-
update(
timss_design ,
one = 1 ,
idcntry = factor( idcntry ) ,
sex = factor( itsex , labels = c( "male" , "female" ) ) ,
born_2005_or_later = as.numeric( itbirthy >= 2005 )
)
```

### Unweighted Counts

Count the unweighted number of records in the survey sample, overall and by groups:

```
MIcombine( with( timss_design , svyby( ~ one , ~ one , unwtd.count ) ) )
MIcombine( with( timss_design , svyby( ~ one , ~ sex , unwtd.count ) ) )
```

### Weighted Counts

Count the weighted size of the generalizable population, overall and by groups:

```
MIcombine( with( timss_design , svytotal( ~ one ) ) )
MIcombine( with( timss_design ,
svyby( ~ one , ~ sex , svytotal )
) )
```

### Descriptive Statistics

Calculate the mean (average) of a linear variable, overall and by groups:

```
MIcombine( with( timss_design , svymean( ~ asmmat ) ) )
MIcombine( with( timss_design ,
svyby( ~ asmmat , ~ sex , svymean )
) )
```

Calculate the distribution of a categorical variable, overall and by groups:

```
MIcombine( with( timss_design , svymean( ~ idcntry ) ) )
MIcombine( with( timss_design ,
svyby( ~ idcntry , ~ sex , svymean )
) )
```

Calculate the sum of a linear variable, overall and by groups:

```
MIcombine( with( timss_design , svytotal( ~ asmmat ) ) )
MIcombine( with( timss_design ,
svyby( ~ asmmat , ~ sex , svytotal )
) )
```

Calculate the weighted sum of a categorical variable, overall and by groups:

```
MIcombine( with( timss_design , svytotal( ~ idcntry ) ) )
MIcombine( with( timss_design ,
svyby( ~ idcntry , ~ sex , svytotal )
) )
```

Calculate the median (50th percentile) of a linear variable, overall and by groups:

```
MIcombine( with( timss_design ,
svyquantile(
~ asmmat ,
0.5 , se = TRUE
) ) )
MIcombine( with( timss_design ,
svyby(
~ asmmat , ~ sex , svyquantile ,
0.5 , se = TRUE ,
keep.var = TRUE , ci = TRUE
) ) )
```

Estimate a ratio:

```
MIcombine( with( timss_design ,
svyratio( numerator = ~ asssci , denominator = ~ asmmat )
) )
```

### Subsetting

Restrict the survey design to Australia, Austria, Azerbaijan, Belgium (French):

`sub_timss_design <- subset( timss_design , idcntry %in% c( 36 , 40 , 31 , 957 ) )`

Calculate the mean (average) of this subset:

`MIcombine( with( sub_timss_design , svymean( ~ asmmat ) ) )`

### Measures of Uncertainty

Extract the coefficient, standard error, confidence interval, and coefficient of variation from any descriptive statistics function result, overall and by groups:

```
this_result <-
MIcombine( with( timss_design ,
svymean( ~ asmmat )
) )
coef( this_result )
SE( this_result )
confint( this_result )
cv( this_result )
grouped_result <-
MIcombine( with( timss_design ,
svyby( ~ asmmat , ~ sex , svymean )
) )
coef( grouped_result )
SE( grouped_result )
confint( grouped_result )
cv( grouped_result )
```

Calculate the degrees of freedom of any survey design object:

`degf( timss_design$designs[[1]] )`

Calculate the complex sample survey-adjusted variance of any statistic:

`MIcombine( with( timss_design , svyvar( ~ asmmat ) ) )`

Include the complex sample design effect in the result for a specific statistic:

```
# SRS without replacement
MIcombine( with( timss_design ,
svymean( ~ asmmat , deff = TRUE )
) )
# SRS with replacement
MIcombine( with( timss_design ,
svymean( ~ asmmat , deff = "replace" )
) )
```

Compute confidence intervals for proportions using methods that may be more accurate near 0 and 1. See `?svyciprop`

for alternatives:

```
MIsvyciprop( ~ born_2001_or_later , timss_design ,
method = "likelihood" , na.rm = TRUE )
```

### Regression Models and Tests of Association

Perform a design-based t-test:

`MIsvyttest( asmmat ~ born_2001_or_later , timss_design )`

Perform a chi-squared test of association for survey data:

`MIsvychisq( ~ born_2001_or_later + idcntry , timss_design )`

Perform a survey-weighted generalized linear model:

```
glm_result <-
MIcombine( with( timss_design ,
svyglm( asmmat ~ born_2001_or_later + idcntry )
) )
summary( glm_result )
```